Upper bound for entropy in asymptotically de Sitter space-time

Maeda, Kenichi; Koike, Tatsuhiko; Narita, Makoto; Ishibashi, Akihiro

doi:10.1103/physrevd.57.3503

Cited by 40 publications

(41 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Ref. [17], the authors have shown that the final values of entropies of the event (S B ) and cosmological (S C ) horizon satisfy the inequality…”

Section: Entropy Of Sdsmentioning

confidence: 99%

“…A naive extension of these approaches to SdS leads us to the conclusions that the SdS has two different temperatures associated with the two horizons. Using this extension, it has been argued [6,17] that the SdS will inevitably evolve towards an empty de Sitter space indicating that SdS may never be in thermodynamic equilibrium with a single temperature associated with the space-time.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Temperature and entropy of Schwarzschild–de Sitter space-time

2003

View full text Add to dashboard Cite

In the light of recent interest in quantum gravity in de Sitter space, we investigate semi-classical aspects of 4-dimensional Schwarzschild-de Sitter space-time using the method of complex paths. The standard semi-classical techniques (such as Bogoliubov coefficients and Euclidean field theory) have been useful to study quantum effects in space-times with single horizons; however, none of these approaches seem to work for Schwarzschild-de Sitter or, in general, for space-times with multiple horizons. We extend the method of complex paths to space-times with multiple horizons and obtain the spectrum of particles produced in these space-times. We show that the temperature of radiation in these space-times is proportional to the effective surface gravity -inverse harmonic sum of surface gravity of each horizon. For the Schwarzschild-de Sitter, we apply the method of complex paths to three different coordinate systems -spherically symmetric, Painleve and Lemaitre. We show that the equilibrium temperature in Schwarzschild-de Sitter is the harmonic mean of cosmological and event horizon temperatures. We obtain Bogoliubov coefficients for space-times with multiple horizons by analyzing the mode functions of the quantum fields near the horizons. We propose a new definition of entropy for space-times with multiple horizons analogous to the entropic definition for space-times with a single horizon. We define entropy for these space-times to be inversely proportional to the square of the effective surface gravity. We show that this definition of entropy for Schwarzschild-de Sitter satisfies the D-bound conjecture.

show abstract

“…In Ref. [17], the authors have shown that the final values of entropies of the event (S B ) and cosmological (S C ) horizon satisfy the inequality…”

Section: Entropy Of Sdsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Temperature and entropy of Schwarzschild–de Sitter space-time

2003

View full text Add to dashboard Cite

show abstract

“…on the BEH, while we leave U unchanged. Since the area of the BEH is non-decreasing and also has an upper bound as shown in [13,14], lim v→∞ R = C 3 , and R ,v ∼ C 4 v −β−1 (β > 0). This means that by Eq.…”

mentioning

confidence: 99%

“…First, we will consider the asymptotic behavior of field functions near the cosmological event horizon (CEH), which is defined as a past Cauchy horizon H − (I + ) when a BEH exists (see Ref. [14]). It is convenient to rescale the coordinate U such that U is an affine parameter of a null geodesic of the CEH, i.e., λ is constant along the CEH.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Do Naked Singularities Generically Occur in Generalized Theories of Gravity?

Terauchi

Narita

1998

Phys. Rev. Lett.

Self Cite

View full text Add to dashboard Cite

A new mechanism for causing naked singularities is found in an effective superstring theory. We investigate the gravitational collapse in a spherically symmetric Einstein-Maxwell-dilaton system in the presence of a pure cosmological constant "potential", where the system has no static black hole solution. We show that once gravitational collapse occurs in the system, naked singularities necessarily appear in the sense that the field equations break down in the domain of outer communications. This suggests that in generalized theories of gravity, the non-minimally coupled fields generically cause naked singularities in the process of gravitational collapse if the system has no static or stationary black hole solution.The singularity theorem [1] states that the occurrence of singularities is inevitable under some physical conditions in general relativity. There are two notable scenarios where singularities may appear in our universe. One is the initial singularity at the birth of the universe and the other is the final stage of gravitational collapse. In the latter case we believe that an event horizon is formed which encloses all occurring singularities as the collapse proceeds, following the cosmic censorship hypothesis (CCH) [2]. CCH is classified into two types, the weak cosmic censorship hypothesis (WCCH) and the strong one (SCCH). WCCH says that observers at an infinity should not see singularities while SCCH says that no observer should see them and the whole region of a space-time can be uniquely determined by initial regular data. Mathematically, SCCH is equivalent to the statement that no Cauchy horizon can be formed in a physical gravitational collapse.Recently many elegant results [3] suggest that SCCH holds for charged and/or rotating black holes due to the destruction of the Cauchy horizon by the mass inflation phenomenon. The general proof of CCH is, however, far from complete and many counter examples have been found in the framework of general relativity [4] Maxwell-dilaton system, which comes from an effective superstring theory, and later Garfinkel, Horowitz and Strominger [6] showed that the inner (Cauchy) horizon in the Reissner-Nordström solution is replaced by a spacelike singularity. This suggests that the occurrence of the inner horizon is not generic and hence SCCH holds if we take the effect of string theory into account. On the other hand Horne and Horowitz [7] obtained the opposite result that extremal electrically charged non-static black hole solutions in the presence of a central charge have timelike singularities. It seems, however, not to be a counter example of SCCH in the sense that such solutions have no regular initial spacelike hypersurface because of the central singularities. Thus, the following question naturally arises. Does CCH really hold in generalized theories of gravity? There is not much evidence deciding the matter yet because the above results do not take any physical process of the gravitational collapse from initial regular data into account. Although a ...

show abstract

An algebra of observables for de Sitter space

Chandrasekaran

Longo

Penington

et al. 2023

J. High Energ. Phys.

View full text Add to dashboard Cite

We describe an algebra of observables for a static patch in de Sitter space, with operators gravitationally dressed to the worldline of an observer. The algebra is a von Neumann algebra of Type II1. There is a natural notion of entropy for a state of such an algebra. There is a maximum entropy state, which corresponds to empty de Sitter space, and the entropy of any semiclassical state of the Type II1 algebras agrees, up to an additive constant independent of the state, with the expected generalized entropy Sgen = (A/4GN) + Sout. An arbitrary additive constant is present because of the renormalization that is involved in defining entropy for a Type II1 algebra.

show abstract

Upper bound for entropy in asymptotically de Sitter space-time

Cited by 40 publications

References 22 publications

Temperature and entropy of Schwarzschild–de Sitter space-time

Temperature and entropy of Schwarzschild–de Sitter space-time

Do Naked Singularities Generically Occur in Generalized Theories of Gravity?

An algebra of observables for de Sitter space

Contact Info

Product

Resources

About