scholarly journals On a Possibly Pure Set-Theoretic Contribution to Black Hole Entropy

2019 ◽  
Vol 25 (2) ◽  
pp. 327-340 ◽  
Author(s):  
Gábor Etesi
Keyword(s):  
Black Hole ◽  
Dimensional Space ◽  
Mathematical Formulation ◽  
Black Hole Entropy ◽  
Conserved Quantities ◽  
Physical Problems ◽  
Dimensional Space Time ◽  
Flow Of Time ◽  
Time Continuum ◽  
The Continuum

Abstract Continuity as appears to us immediately by intuition (in the flow of time and in motion) differs from its current formalization, the arithmetical continuum or equivalently the set of real numbers used in modern mathematical analysis. Motivated by the known mathematical and physical problems arising from this formalization of the continuum, our aim in this paper is twofold. Firstly, by interpreting Chaitin’s variant of Gödel’s first incompleteness theorem as an inherent uncertainty or fuzziness of the arithmetical continuum, a formal set-theoretic entropy is assigned to the arithmetical continuum. Secondly, by analyzing Noether’s theorem on symmetries and conserved quantities, we argue that whenever the four dimensional space-time continuum containing a single, stationary, asymptotically flat black hole is modeled by the arithmetical continuum in the mathematical formulation of general relativity, the hidden set-theoretic entropy of this latter structure reveals itself as the entropy of the black hole (proportional to the area of its “instantaneous” event horizon), indicating that this apparently physical quantity might have a pure set-theoretic origin, too.

scholarly journals ON KALUZA–KLEIN SPACE–TIME IN EINSTEIN–GAUSS–BONNET GRAVITY

2009 ◽  
Vol 18 (04) ◽  
pp. 599-611 ◽  
Author(s):  
ALFRED MOLINA ◽  
NARESH DADHICH
Keyword(s):  
Black Hole ◽  
Black Hole Solution ◽  
Dimensional Space ◽  
Space Time ◽  
Two Dimensional ◽  
Bonnet Gravity ◽  
Space Of Constant Curvature ◽  
Dimensional Black Hole ◽  
Dimensional Space Time ◽  
Kaluza Klein

By considering the product of the usual four-dimensional space–time with two dimensional space of constant curvature, an interesting black hole solution has recently been found for Einstein–Gauss–Bonnet gravity. It turns out that this as well as all others could easily be made to radiate Vaidya null dust. However, there exists no Kerr analog in this setting. To get the physical feel of the four-dimensional black hole space–times, we study asymptotic behavior of stresses at the two ends, r → 0 and r → ∞.

scholarly journals Proton decay and the quantum structure of space–time

2019 ◽  
Vol 97 (12) ◽  
pp. 1317-1322
Author(s):  
Abeer Al-Modlej ◽  
Salwa Alsaleh ◽  
Hassan Alshal ◽  
Ahmed Farag Ali
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Coherent State ◽  
Dimensional Space ◽  
Space Time ◽  
Noncommutative Space ◽  
Quantum Structure ◽  
Dimensional Space Time ◽  
Proton Lifetime ◽  
Virtual Black Holes

Virtual black holes in noncommutative space–time are investigated using coordinate coherent state formalism such that the event horizon of a black hole is manipulated by smearing it with a Gaussian of width [Formula: see text], where θ is the noncommutativity parameter. Proton lifetime, the main associated phenomenology of the noncommutative virtual black holes, has been studied, first in four-dimensional space–time and then generalized to D dimensions. The lifetime depends on θ and the number of space–time dimensions such that it emphasizes on the measurement of proton lifetime as a potential probe for the microstructure of space–time.

scholarly journals Emergence of Time in Quantum Gravity: Is Time Necessarily Flowing?

KronoScope ◽  
2013 ◽  
Vol 13 (1) ◽  
pp. 67-84 ◽  
Author(s):  
Pierre Martinetti
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Proper Time ◽  
Dimensional Space ◽  
Thermal Time ◽  
List Type ◽  
State Dependent ◽  
Dimensional Space Time ◽  
Flow Of Time ◽  
Time In Quantum Mechanics

Abstract We discuss the emergence of time in quantum gravity and ask whether time is always “something that flows.” We first recall that this is indeed the case in both relativity and quantum mechanics, although in very different manners: time flows geometrically in relativity (i.e., as a flow of proper time in the four dimensional space-time), time flows abstractly in quantum mechanics (i.e., as a flow in the space of observables of the system). We then ask the same question in quantum gravity in the light of the thermal time hypothesis of Connes and Rovelli. The latter proposes to answer the question of time in quantum gravity (or at least one of its many aspects) by postulating that time is a state-dependent notion. This means that one is able to make a notion of time as an abstract flow—that we call the thermal time—emerge from the knowledge of both: the algebra of observables of the physical system under investigation; a state of thermal equilibrium of this system. Formally, the thermal time is similar to the abstract flow of time in quantum mechanics, but we show in various examples that it may have a concrete implementation either as a geometrical flow or as a geometrical flow combined with a non-geometric action. This indicates that in quantum gravity, time may well still be “something that flows” at some abstract algebraic level, but this does not necessarily imply that time is always and only “something that flows” at the geometric level.

Tunneling in Horava–Lifshitz black hole

2013 ◽  
Vol 91 (1) ◽  
pp. 64-70 ◽  
Author(s):  
J. Sadeghi ◽  
A. Banijamali ◽  
E. Reisi
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Dimensional Space ◽  
Null Geodesic ◽  
Hawking Temperature ◽  
Jacobi Method ◽  
Back Reaction ◽  
Dimensional Space Time ◽  
Lifshitz Black Holes ◽  
Lifshitz Black Hole

In this paper, using the Hamilton–Jacobi method we first calculate the Hawking temperature for a Horava–Lifshitz black hole. Then by utilizing the radial null geodesic method we obtain the entropy of such a black hole in four-dimensional space–time. We also consider the effect of back reaction on the surface gravity and compute modifications of entropy and Hawking temperature because of such an effect. Our calculations are for two kinds of Horava–Lifshitz black holes: Kehagias–Sfetsos and Lu–Mei–Pope.

ON (2+2)-DIMENSIONAL SPACE–TIMES, STRINGS AND BLACK HOLES

2007 ◽  
Vol 22 (11) ◽  
pp. 2021-2045 ◽  
Author(s):  
C. CASTRO ◽  
J. A. NIETO
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Homogeneous Spaces ◽  
Dimensional Space ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Dimensional Solution ◽  
Complex Dimensions ◽  
Dimensional Space Time ◽  
Dimensional Boundary

We study black hole-like solutions (space–times with singularities) of Einstein field equations in 3+1 and 2+2 dimensions. We find three different cases associated with hyperbolic homogeneous spaces. In particular, the hyperbolic version of Schwarzschild's solution contains a conical singularity at r = 0 resulting from pinching to zero size r = 0 the throat of the hyperboloid [Formula: see text] and which is quite different from the static spherically symmetric (3+1)-dimensional solution. Static circular symmetric solutions for metrics in 2+2 are found that are singular at ρ = 0 and whose asymptotic ρ→∞ limit leads to a flat (1+2)-dimensional boundary of topology S1 × R2. Finally we discuss the (1+1)-dimensional Bars–Witten stringy black hole solution and show how it can be embedded into our (3+1)-dimensional solutions. Black holes in a (2+2)-dimensional "space–time" from the perspective of complex gravity in 1+1 complex dimensions and their quaternionic and octonionic gravity extensions deserve furher investigation. An appendix is included with the most general Schwarzschild-like solutions in D ≥ 4.

scholarly journals Deviations of the “Hubble Constant” Value within a “Spherical Gravitational Indentation of approximately 10-10 [m/s2 ]” surrounding our Milky Way Galaxy” in a 4-dimensional Space-Time Continuum.

2021 ◽  
Author(s):  
Wim Vegt
Keyword(s):  
General Relativity ◽  
Fine Structure ◽  
Milky Way ◽  
Dimensional Space ◽  
Hubble Constant ◽  
Space Time ◽  
Milky Way Galaxy ◽  
Dimensional Space Time ◽  
Time Continuum ◽  
Made In

The “Hubble Constant” Value and specially the deviations in the “Hubble Constant” Value are one of the most fundamental parameters in our universe to understand the fine-structure of our 4-dimensional Space-Time continuum. Recent measurements with the “HST” of the “Hubble Constant” and the measured deviations[Ref. 17] reveal fundamental information of the fine-structure of our 4-dimensional Space-Time continuum. The recent measurements reveal a “Spherical Gravitational Indentation of approximately 10-10 [m/s2 ] with a diameter of approximately 2000 Mpc” surrounding our solar Milky Way Galaxy”. With increasing accuracies the need increases of a “New Theory in Physics” to explain the measured anomalies in the “Hubble Constant” value. Because “General Relativity” is not enough anymore to solve the nowadays problems in physics and specially in astronomy. With increasing accuracies the anomalies in the “Hubble Constant” value only become clearer. To develop a “New Theory in Physics” fundamental corrections have to be made in 2 of the 4 foundations in Physics. Corrections have to be made in Maxwell’s Electrodynamics and Bohr’s Quantum Mechanics. General Relativity will developed further to built the new theory in physics. Newton’s Classical dynamics will remain like it has always been. A solid ground to built on. Isaac Newton, James Clerk Maxwell, Niels Bohr and Albert Einstein lived in fundamentally different time frames. Newton in the 16th century, Maxwell in the 18th century, Bohr in the 20th century and Einstein was physically living in the 20th century but he was his time far ahead and with his concept of a “curved space-time continuum” more connected to the 21st century.

scholarly journals A-topology for Minkowski space

1979 ◽  
Vol 21 (1) ◽  
pp. 53-64 ◽  
Author(s):  
Sribatsa Nanda
Keyword(s):  
Minkowski Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
One Dimensional ◽  
Group Of Homeomorphisms ◽  
Dimensional Space Time ◽  
The One ◽  
Induced Topology ◽  
Time Continuum ◽  
Inhomogeneous Lorentz Group

AbstractWe consider in this paper a topology (which we call the A-topology) on Minkowski space, the four-dimensional space–time continuum of special relativity and derive its group of homeomorphisms. We define the A-topology to be the finest topology on Minkowski space with respect to which the induced topology on time-like and light-like lines is one-dimensional Euclidean and the induced topology on space-like hyperplanes is three- dimensional Euclidean. It is then shown that the group of homeomorphisms of this topology is precisely the one generated by the inhomogeneous Lorentz group and the dilatations.

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