On the speed of a test particle inside the Schwarzschild event horizon and other kinds of black holes

A test particle falling onto a classical black hole crosses the event horizon and ends up in the singularity within finite eigentime. In the "more realistic" case of a "classical" evaporating black hole, an observer falling onto a black hole observes a sudden evaporation of the hole. This illustrates the fact that the discussion of the classical process, commonly found in the literature, may become obsolete when the black hole has a finite lifetime. The situation is basically the same for more complex cases, for example, where a particle collides with two merging black holes. It should be pointed out that the model used in this paper is mainly of academic interest, since the description of the physics near a black-hole horizon still presents a difficult problem that is not yet fully understood, but our model provides a valuable possibility for students to enter the interesting field of black-hole physics and to perform numerical calculations of their own that are not very involved from the computational point of view.PACS Nos.: 04.25.g, 04.70.s, 04.70.Dy

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Beyond the Schwarzschild Metric

10.1093/oso/9780199658633.003.0019 ◽

2018 ◽

Author(s):

David M. Wittman

Keyword(s):

Black Holes ◽

General Relativity ◽

Gravitational Waves ◽

Test Particle ◽

Direct Detection ◽

Relativistic Effects ◽

Big Bang ◽

Clusters Of Galaxies ◽

General Relativistic ◽

The Universe

General relativity explains much more than the spacetime around static spherical masses.We briefly assess general relativity in the larger context of physical theories, then explore various general relativistic effects that have no Newtonian analog. First, source massmotion gives rise to gravitomagnetic effects on test particles.These effects also depend on the velocity of the test particle, which has substantial implications for orbits around black holes to be further explored in Chapter 20. Second, any changes in the sourcemass ripple outward as gravitational waves, and we tell the century‐long story from the prediction of gravitational waves to their first direct detection in 2015. Third, the deflection of light by galaxies and clusters of galaxies allows us to map the amount and distribution of mass in the universe in astonishing detail. Finally, general relativity enables modeling the universe as a whole, and we explore the resulting Big Bang cosmology.

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Event Horizon Telescope observations of the jet launching and collimation in Centaurus A

Nature Astronomy ◽

10.1038/s41550-021-01417-w ◽

2021 ◽

Author(s):

Michael Janssen ◽

Heino Falcke ◽

Matthias Kadler ◽

Eduardo Ros ◽

Maciek Wielgus ◽

...

Keyword(s):

Black Holes ◽

Event Horizon ◽

Galactic Nuclei ◽

Galactic Centre ◽

Radio Jets ◽

Long Baseline ◽

Wide Range ◽

Terahertz Frequencies ◽

Source Structure ◽

Centaurus A

AbstractVery-long-baseline interferometry (VLBI) observations of active galactic nuclei at millimetre wavelengths have the power to reveal the launching and initial collimation region of extragalactic radio jets, down to 10–100 gravitational radii (rg ≡ GM/c2) scales in nearby sources1. Centaurus A is the closest radio-loud source to Earth2. It bridges the gap in mass and accretion rate between the supermassive black holes (SMBHs) in Messier 87 and our Galactic Centre. A large southern declination of −43° has, however, prevented VLBI imaging of Centaurus A below a wavelength of 1 cm thus far. Here we show the millimetre VLBI image of the source, which we obtained with the Event Horizon Telescope at 228 GHz. Compared with previous observations3, we image the jet of Centaurus A at a tenfold higher frequency and sixteen times sharper resolution and thereby probe sub-lightday structures. We reveal a highly collimated, asymmetrically edge-brightened jet as well as the fainter counterjet. We find that the source structure of Centaurus A resembles the jet in Messier 87 on ~500 rg scales remarkably well. Furthermore, we identify the location of Centaurus A’s SMBH with respect to its resolved jet core at a wavelength of 1.3 mm and conclude that the source’s event horizon shadow4 should be visible at terahertz frequencies. This location further supports the universal scale invariance of black holes over a wide range of masses5,6.

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Black Holes or an Objects without Event Horizon?

10.20944/preprints202103.0575.v2 ◽

2021 ◽

Author(s):

Leonid Verozub

Keyword(s):

Black Holes ◽

Event Horizon ◽

Fermi Gas ◽

Einstein’S Equations ◽

Einstein's Equations ◽

Degenerate Fermi Gas

The paper substantiates the possibility that objects that we usually identify with black holes are self-gravitating, fully or partially degenerate Fermi gas. This follows from the modification of Einstein's equations, which is based on a mathematical fact that the author of the GR could not have known in his time.

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LUKEWARM BLACK HOLES IN QUADRATIC GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732311035560 ◽

2011 ◽

Vol 26 (14) ◽

pp. 999-1007 ◽

Cited By ~ 6

Author(s):

JERZY MATYJASEK ◽

KATARZYNA ZWIERZCHOWSKA

Keyword(s):

Black Holes ◽

Black Hole ◽

Event Horizon ◽

Fourth Order ◽

Spherically Symmetric ◽

Cosmological Horizon ◽

De Sitter ◽

Quadratic Gravity ◽

De Sitter Universe ◽

Electrically Charged

Perturbative solutions to the fourth-order gravity describing spherically-symmetric, static and electrically charged black hole in an asymptotically de Sitter universe is constructed and discussed. Special emphasis is put on the lukewarm configurations, in which the temperature of the event horizon equals the temperature of the cosmological horizon.

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Change in event horizon surface area as the source of nonmetricity field

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887818501049 ◽

2018 ◽

Vol 15 (06) ◽

pp. 1850104

Author(s):

Yuriy A. Portnov

Keyword(s):

Black Holes ◽

Surface Area ◽

Event Horizon ◽

Test Body ◽

Body Motion ◽

Motion Equations ◽

Gravitational Source ◽

Theory Of Gravitation ◽

The Relationship ◽

Over Time

This paper concerns the relationship between the nonmetricity 1-form and the change in entropy. Motion equations have been obtained for test bodies in a gravitational field created by a massive body with entropy varying over time. It has been shown that increasing entropy of the gravitational source will bring about an increase in the acceleration of the test body. Applied to the theory of gravitation with nonmetricity, black hole dynamics equations based on foundations laid by S. Hawking and J. Beckenstein, enabled identification of changes in black holes event horizon surface area as a putative source of nonmetricity field. The implication is that changes in event horizon area will affect test body motion. The latter property makes it possible to contemplate a completely new method for discovering short-lived microscopic black holes.

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3. Extrasolar tests of gravity

Gravity: A Very Short Introduction ◽

10.1093/actrade/9780198729143.003.0003 ◽

2017 ◽

pp. 35-45

Author(s):

Timothy Clifton

Keyword(s):

Black Holes ◽

Black Hole ◽

Gravitational Field ◽

Solar System ◽

Neutron Stars ◽

Event Horizon ◽

Gravitational Fields ◽

Binary Pulsars ◽

Tests Of Gravity ◽

Triple Star

By studying objects outside our Solar System, we can observe star systems with far greater gravitational fields. ‘Extrasolar tests of gravity’ considers stars of different sizes that have undergone gravitational collapse, including white dwarfs, neutron stars, and black holes. A black hole consists of a region of space-time enclosed by a surface called an event horizon. The gravitational field of a black hole is so strong that anything that finds its way inside the event horizon can never escape. Other star systems considered are binary pulsars and triple star systems. With the invention of even more powerful telescopes, there will be more tantalizing possibilities for testing gravity in the future.

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Entropy bound of horizons of some regular black holes

Modern Physics Letters A ◽

10.1142/s0217732320500704 ◽

2020 ◽

Vol 35 (10) ◽

pp. 2050070

Author(s):

Ujjal Debnath

Keyword(s):

Black Holes ◽

Heat Capacity ◽

Black Hole ◽

Specific Heat ◽

Surface Area ◽

Event Horizon ◽

Specific Heat Capacity ◽

Thermodynamic Quantities ◽

Event Horizons ◽

Regular Black Hole

We study the four-dimensional (i) modified Bardeen black hole, (ii) modified Hayward black hole, (iii) charged regular black hole and (iv) magnetically charged regular black hole. For modified Bardeen black hole and modified Hayward black hole, we found only one horizon (event horizon) and then we found some thermodynamic quantities like the entropy, surface area, irreducible mass, temperature, Komar energy and specific heat capacity on the event horizon. We here study the bounds of the above thermodynamic quantities for these black holes on the event horizon. Then, we examine the thermodynamics stability of the black holes with some conditions. Next, we studied the charged regular black hole and magnetically charged regular black hole and found two horizons (Cauchy and event horizons) of these black holes. Then, we found the entropy, surface area, irreducible mass, temperature, Komar energy and specific heat capacity on the Cauchy and event horizons. Then, we get some conditions for thermodynamic stability/instability of the black holes. We found the radius of the extremal horizon and Christodoulou–Ruffiini mass and then analyze the above thermodynamic quantities on the extremal horizon. We calculate the sum/subtraction, product, division and sum/subtraction of inverse of surface areas, entropies, irreducible masses, temperatures, Komar energies and specific heat capacities on both the horizons. From these, we found the bounds of the above quantities on the horizons.

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Launching proton-dominated jets from accreting Kerr Black Holes: the case of M87

Astronomy Studies Development ◽

10.4081/asd.2011.e4 ◽

2011 ◽

Vol 1 (1) ◽

pp. 4 ◽

Cited By ~ 1

Author(s):

Felix F. Brezinski ◽

Ahmad A. Hujeirat

Keyword(s):

Magnetic Field ◽

Boundary Layer ◽

Black Holes ◽

Angular Momentum ◽

Event Horizon ◽

Accretion Disk ◽

Lorentz Factor ◽

Spin Parameter ◽

Low Mass ◽

Kerr Black Holes

A general relativistic model for the formation and acceleration of low mass-loaded jets from systems containing accreting black holes is presented. The model is based on previous numerical results and theoretical studies in the Newtonian regime, but modified to include the effects of space-time curvature in the vicinity of the event horizon of a spinning black hole. It is argued that the boundary layer between the Keplerian accretion disk and the event horizon is best suited for the formation and acceleration of the accretion-powered jets in active galactic nuclei and micro-quasars. The model presented here is based on matching the solutions of three different regions: i- a weakly magnetized Keplerian accretion disk in the outer part, where the transport of angular momentum is mediated through the magentorotational instability, ii- a strongly magnetized, advection-dominated and turbulent-free boundary layer (BL) between the outer cold accretion disk and the event horizon and where the plasma rotates sub-Keplerian and iii- a transition zone (TZ) between the BL and the overlying corona, where the electrons and protons are thermally uncoupled, highly dissipative and rotate super-Keplerian. In the BL, the gravitation-driven dynamical collapse of the plasma increases the strength of the poloidal magnetic field (PMF) significantly, subsequently suppressing the generation and dissipation of turbulence and turning off the primary source of heating. In this case, the BL appears much fainter than standard disk models so as if the disk truncates at a certain radius. The action of the PMF in the BL is to initiate torsional Alf`ven waves that transport angular momentum from the embedded plasma vertically into the TZ, where a significant fraction of the shear-generated toroidal magnetic field reconnects, thereby heating the protons up to the virial-temperature. Also, the strong PMF forces the electrons to cool rapidly, giving rise therefore to the formation of a gravitationally unbound two-temperature proton-dominated outflow. Our model predicts the known correlation between the Lorentz-factor and the spin parameter of the BH. It also shows that the effective surface of the BL, through which the baryons flow into the TZ, shrinks with increasing the spin parameter, implying therefore that low mass-loaded jets most likely originate from around Kerr black holes. When applying our model to the jet in the elliptical galaxy M87, we find a spin parameter <em>a ∈</em> [0.99, 0.998], a transition radius rtr ≈ 30 gravitational radii and a fraction of 0.05 − 0.1 of the mass accretion rate goes into the TZ, where the plasma speeds up its outward-oriented motion to reach a Lorentz factor Γ <em>∈</em> [2.5, 5.0] at rtr.

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More on extracting information about the initial state from the black hole radiation

Modern Physics Letters A ◽

10.1142/s0217732318501080 ◽

2018 ◽

Vol 33 (19) ◽

pp. 1850108

Author(s):

Hossein Ghaforyan ◽

Somayyeh Shoorvazi ◽

Alireza Sepehri ◽

Tooraj Ghaffary

Keyword(s):

Black Holes ◽

Black Hole ◽

Density Matrix ◽

Quantum Entanglement ◽

Event Horizon ◽

Initial State ◽

Black Hole Radiation ◽

Total Information ◽

Quantum Treatment ◽

Collapse Process

Recently, some authors showed that a classical collapse scenario ignores this richness of information in the resulting spectrum and a consistent quantum treatment of the entire collapse process might allow us to retrieve much more information from the spectrum of the final radiation. We confirm these results and show that by considering the quantum entanglement between metrics, we can uncover information of black holes. In our model, a density matrix is defined for the spaces, both inside and outside of the event horizon. These inside and outside spaces of black holes are obtained by tracing from a bigger space. An observer that lives in this big space can recover total information regarding the inside and outside of black hole.

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