The Wheeler–Dewitt Equation for the Superstring World Sheet

1997 ◽  
Vol 06 (01) ◽  
pp. 91-105 ◽  
Author(s):  
M. D. Pollock
Keyword(s):  
Black Hole ◽  
Ground State ◽  
Total Mass ◽  
Equation Of Motion ◽  
Schwarzschild Black Hole ◽  
World Sheet ◽  
Integral Expression ◽  
Higher Derivative ◽  
The World ◽  
The Universe

The Wheeler–DeWitt equation for the wave function ψ is obtained from the two-dimensional world-sheet action for the bosonic string and the superstring, including higher-derivative terms, as the Schrödinger equation i ∂ ψ/ ∂τ = V(τ)ψ. The potential is given by the rate at which the world-sheet area is swept out, V(τ) = dA(τ)/dτ, and is positive semi-definite, allowing the existence of a ground state, corresponding to the absence of the string, with a non-vanishing probability density ψ ψ*. Integration of this equation yields the solution [Formula: see text], where [Formula: see text] is the action, minus the higher-derivative terms [Formula: see text] (and terms involving ∊ab in the case of the superstring), which, however, are constrained to vanish semi-classically, being constructed from the square of the equation of motion for the bosonic coordinates XA derived from [Formula: see text] alone. This path-integral expression for ψ is consistent with the operator replacements for the canonical momenta used in its derivation, and forms the basis of the approach due to Polyakov of summing over random surfaces. Comparison is made with the Schrödinger equations derived previously from the reduced, four-dimensional effective action for the heterotic superstring, and for the Schwarzschild black hole (by Tomimatsu), where the potential is also positive semi-definite, being (twice) the total mass of the Universe and the mass of the black hole, respectively, showing the unity of the method.

The Odd Couple: Quasars & Black Holes

Daedalus ◽  
2014 ◽  
Vol 143 (4) ◽  
pp. 103-113 ◽  
Author(s):  
Scott Tremaine
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Solar System ◽  
Total Mass ◽  
Host Galaxy ◽  
The Sun ◽  
Central Black Hole ◽  
Frictional Forces ◽  
The Universe

Quasars emit more energy than any other object in the universe, yet are not much bigger than our solar system. Quasars are powered by giant black holes of up to ten billion (1010) times the mass of the sun. Their enormous luminosities are the result of frictional forces acting upon matter as it spirals toward the black hole, heating the gas until it glows. We also believe that black holes of one million to ten billion solar masses – dead quasars – are present at the centers of most galaxies, including our own. The mass of the central black hole appears to be closely related to other properties of its host galaxy, such as the total mass in stars, but the origin of this relation and the role that black holes play in the formation of galaxies are still mysteries.

scholarly journals QUANTUM EFFECTS AND STABILITY OF CHAMELEON COSMOLOGY

2004 ◽  
Vol 19 (17) ◽  
pp. 1273-1280 ◽  
Author(s):  
SHIN'ICHI NOJIRI ◽  
SERGEI D. ODINTSOV
Keyword(s):  
Quantum Effects ◽  
Equation Of Motion ◽  
Matter Density ◽  
Accelerated Expansion ◽  
Conformal Anomaly ◽  
Tensor Theory ◽  
Higher Derivative ◽  
Expansion Of The Universe ◽  
The Universe ◽  
Principal Possibility

One possibility to explain the current accelerated expansion of the universe may be related with the presence of cosmologically evolving scalar whose mass depends on the local matter density (chameleon cosmology). We point out that matter quantum effects in such scalar–tensor theory produce the chameleon scalar field dependent conformal anomaly. Such conformal anomaly adds higher derivative terms to chameleon field equation of motion. As a result, the principal possibility for instabilities appears. These instabilities seem to be irrelevant at small curvature but may become dangerous in the regions where gravitational field is strong.

scholarly journals Thermodynamics of a Black Hole

2015 ◽  
Vol 48 ◽  
pp. 123-137
Author(s):  
K.A.I.L. Wijewardena Gamalath ◽  
N.S. Rajapakse
Keyword(s):  
Black Hole ◽  
Visible Region ◽  
Black Hole Entropy ◽  
Mass Variation ◽  
Schwarzschild Black Hole ◽  
Black Hole Evaporation ◽  
Time Variations ◽  
The Given ◽  
The Universe ◽  
Over Time

A simple model was setup to find the mass variation over time for a Schwarzschild black hole. The temperature and entropy of a black hole was obtained from the numerically solved mass variation and the time variations of the black hole thermodynamic parameters were simulated. The mass of a given black hole reduces rapidly. The time taken for a black hole to vanish increases in an increasing rate with the given initial mass of the black hole. The temperature of a black hole drastically increases at the final stage of the black hole evaporation. The colour attributed to that temperature was found to be in the visible region for a significant amount of time. The black hole entropy also drastically reduces with its mass and through Hawking radiation it is added to the rest of the universe.

On the internal state of the Schwarzschild black hole

2017 ◽  
Vol 26 (09) ◽  
pp. 1750088
Author(s):  
M. D. Pollock
Keyword(s):  
Black Hole ◽  
Internal State ◽  
Energy Condition ◽  
Momentum Tensor ◽  
Schwarzschild Black Hole ◽  
Superstring Theory ◽  
Higher Derivative ◽  
Central Singularity ◽  
Symmetric Line ◽  
Tensor Formula

If the classical gravitational Lagrangian contains higher-derivative terms [Formula: see text], where [Formula: see text], then vacuum solutions of the Einstein–Hilbert theory [Formula: see text] are subject to modification at sufficiently large spacetime curvatures. Previously, we have calculated the effective energy–momentum tensor [Formula: see text] due to the quartic gravitational terms [Formula: see text] of the heterotic superstring theory in the four-dimensional background spacetime of the Schwarzschild black hole, obtaining an expression which satisfies the strong energy condition, and thereby suggests that the [Formula: see text] might not remove the central singularity. This conjecture was put forward from a different viewpoint by Horowitz and Myers, who argued that a non-singular black-hole interior resulting from the [Formula: see text] would be unstable, necessitating reappraisal of the notion of a singular interior spacetime. Here, we show that the chief features of the solution can be simulated by a Bardeen-type ansatz, assuming the spherically symmetric line element [Formula: see text], where [Formula: see text], which, when [Formula: see text], can explain heuristically why [Formula: see text] in the shell region [Formula: see text] of a macroscopic black hole for which [Formula: see text], while [Formula: see text] remains finite at [Formula: see text].

scholarly journals HOLOGRAPHIC ENTROPY AND BRANE FRW DYNAMICS FROM AdS BLACK HOLE IN d5 HIGHER DERIVATIVE GRAVITY

2001 ◽  
Vol 16 (31) ◽  
pp. 5085-5099 ◽  
Author(s):  
SHIN'ICHI NOJIRI ◽  
SERGEI D. ODINTSOV ◽  
SACHIKO OGUSHI
Keyword(s):  
Black Hole ◽  
Gravitational Constant ◽  
Scale Parameter ◽  
Riemann Tensor ◽  
Schwarzschild Black Hole ◽  
Strongly Coupled ◽  
Verlinde Formula ◽  
Higher Derivative ◽  
Entropy Bounds ◽  
Tensor Square

Higher derivative bulk gravity (without Riemann tensor square term) admits AdS–Schwarzschild black hole as an exact solution. It is shown that induced brane geometry on such background is open, flat or closed FRW radiation dominated universe. Higher derivative terms contributions appear in the Hawking temperature, entropy and Hubble parameter via the redefinition of five-dimensional gravitational constant and AdS scale parameter. These higher derivative terms do not destroy the AdS-dual description of radiation represented by strongly-coupled CFT. The Cardy–Verlinde formula which expresses cosmological entropy as the square root from other parameters and entropies is derived in R2gravity. The corresponding cosmological entropy bounds are briefly discussed.

scholarly journals Can accretion properties distinguish between a naked singularity, wormhole and black hole?

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
R. Kh. Karimov ◽  
R. N. Izmailov ◽  
A. A. Potapov ◽  
K. K. Nandi
Keyword(s):  
Black Hole ◽  
Naked Singularity ◽  
Singular Limit ◽  
Jordan Frame ◽  
Coordinate Transformations ◽  
Wick Rotation ◽  
Schwarzschild Black Hole ◽  
Particle Orbits ◽  
Stable Radius ◽  
The Universe

AbstractWe first advance a mathematical novelty that the three geometrically and topologically distinct objects mentioned in the title can be exactly obtained from the Jordan frame vacuum Brans I solution by a combination of coordinate transformations, trigonometric identities and complex Wick rotation. Next, we study their respective accretion properties using the Page–Thorne model which studies accretion properties exclusively for $$r\ge r_{\text {ms}}$$ r ≥ r ms (the minimally stable radius of particle orbits), while the radii of singularity/throat/horizon $$r<r_{\text {ms}}$$ r < r ms . Also, its Page–Thorne efficiency $$\epsilon $$ ϵ is found to increase with decreasing $$r_{\text {ms}}$$ r ms and also yields $$\epsilon =0.0572$$ ϵ = 0.0572 for Schwarzschild black hole (SBH). But in the singular limit $$r\rightarrow r_{s}$$ r → r s (radius of singularity), we have $$\epsilon \rightarrow 1$$ ϵ → 1 giving rise to $$100 \%$$ 100 % efficiency in agreement with the efficiency of the naked singularity constructed in [10]. We show that the differential accretion luminosity $$\frac{d{\mathcal {L}}_{\infty }}{d\ln {r}}$$ d L ∞ d ln r of Buchdahl naked singularity (BNS) is always substantially larger than that of SBH, while Eddington luminosity at infinity $$L_{\text {Edd}}^{\infty }$$ L Edd ∞ for BNS could be arbitrarily large at $$r\rightarrow r_{s}$$ r → r s due to the scalar field $$\phi $$ ϕ that is defined in $$(r_{s}, \infty )$$ ( r s , ∞ ) . It is concluded that BNS accretion profiles can still be higher than those of regular objects in the universe.

scholarly journals SPACE TIME FOAM

2002 ◽  
Vol 17 (06n07) ◽  
pp. 829-832 ◽  
Author(s):  
REMO GARATTINI
Keyword(s):  
Black Hole ◽  
Cosmological Constant ◽  
Ground State ◽  
Casimir Energy ◽  
Space Time ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Positive Cosmological Constant ◽  
Hole Transition

In the context of a model of space-time foam, made by N wormholes we discuss the possibility of having a foam formed by different configurations. An equivalence between Schwarzschild and Schwarzschild-Anti-de Sitter wormholes in terms of Casimir energy is shown. An argument to discriminate which configuration could represent a foamy vacuum coming from Schwarzschild black hole transition frequencies is used. The case of a positive cosmological constant is also discussed. Finally, a discussion involving charged wormholes leads to the conclusion that they cannot be used to represent a ground state of the foamy type.

scholarly journals On causal structure of 4D-Einstein–Gauss–Bonnet black hole

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Naresh Dadhich
Keyword(s):  
Black Hole ◽  
Black Hole Solution ◽  
Causal Structure ◽  
Equation Of Motion ◽  
Cauchy Horizon ◽  
Coupling Constant ◽  
Schwarzschild Black Hole ◽  
Effective Equation ◽  
Central Singularity ◽  
Static Black Hole

AbstractThe recently proposed effective equation of motion for the 4D-Einstein–Gauss–Bonnet gravity admits a static black hole solution that has, like the Rissner–Nordström charged black hole, two horizons instead of one for the Schwarzschild black hole. This means that the central singularity is timelike instead of spacelike. It should though be noted that in $$D\ge 5$$ D ≥ 5 , the solution always admits only one horizon like the Schwarzshild solution. In the equation defining the horizon, the rescaled Gauss–Bonnet coupling constant appears as a new ‘gravitational charge’ with a repulsive effect to cause in addition to event horizon a Cauchy horizon. Thus it radically alters the causal structure of the black hole.

Sign in / Sign up

Export Citation Format

Share Document