Apparent horizon and gravitational thermodynamics of the Universe: Solutions to the temperature and entropy confusions and extensions to modified gravity

Tian, David Wenjie; Booth, Ivan

doi:10.1103/physrevd.92.024001

Cited by 35 publications

(40 citation statements)

References 120 publications

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“…Attempts to build thermodynamics by associating entropy and temperature with such horizons can be seen in, e.g. [33][34][35] and in references therein. However, we note that unlike the Killing horizons, the Hubble or apparent horizon is not a null surface in general [36] as the normal to such surfaces, ∇ a (r(t)H(t)), is not in general a null vector.In the usual statistical mechanics of normal matter, the entropy depends upon the volume of the system, instead of its area.…”

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confidence: 99%

Entropy of a box of gas in an external gravitational field revisited

2017

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Earlier it was shown that the entropy of an ideal gas, contained in a box and moving in a gravitational field, develops an area dependence when it approaches the horizon of a static, spherically symmetric spacetime. Here we extend the above result in two directions; viz., to (a) the stationary axisymmteric spacetimes and (b) time dependent cosmological spacetimes evolving asymptotically to the de Sitter or the Schwarzschild de Sitter spacetimes. While our calculations are exact for the stationary axisymmetric spacetimes, for the cosmological case we present an analytical expression of the entropy when the spacetime is close to the de Sitter or the Schwarzschild de Sitter spacetime. Unlike the static spacetimes, there is no hypersurface orthogonal timelike Killing vector field in these cases. Nevertheless, the results hold and the entropy develops an area dependence in the appropriate limit.necessarily Killing horizons, the observers who do not cross them would still associate entropy densities (1/4) with the relevant areas.Given that the black holes have thermodynamic properties, it is natural to ask whether such notions could be associated with cosmological or Hubble horizons as well. Among them, perhaps the most interesting one is that of the de Sitter space, which has a Killing horizon. The de Sitter horizon could also be associated with thermodynamic properties such as the entropy and temperature, qualitatively similar to that of the black hole [28][29][30][31][32]. For cosmological spacetimes other than the de Sitter, the Hubble horizon, r(t) = H −1 (t) (where t is the comoving time, r(t) is the proper radius and H(t) is the Hubble rate) is not a Killing horizon. For a spatially flat cosmology, the Hubble horizon also coincides with the apparent horizon, where the expansion corresponding to one of the two principle null congruences vanishes while the other being positive. The notion of apparent horizon is dependent upon the spacetime foliation. Attempts to build thermodynamics by associating entropy and temperature with such horizons can be seen in, e.g. [33][34][35] and in references therein. However, we note that unlike the Killing horizons, the Hubble or apparent horizon is not a null surface in general [36] as the normal to such surfaces, ∇ a (r(t)H(t)), is not in general a null vector.In the usual statistical mechanics of normal matter, the entropy depends upon the volume of the system, instead of its area. Thus, the horizons are indeed some special objects -qualitatively or quantitatively, as far as the thermodynamic properties are concerned. It was shown in [37,38] that in order for the entropy-area relation to hold, the density of states near the horizon must have an exponential 'pile up' behaviour and any effective theory describing a quantum field near the horizon must be non-local, over the Planck length scale near the horizon. In [39], the dynamics of a box containing an ideal gas moving in a static and spherically symmetric black hole spacetime was considered and the area dependence of the entro...

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confidence: 99%

Entropy of a box of gas in an external gravitational field revisited

2017

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“…(8), and also similar attempts such as those introduced in Refs. [9,10,16,24]. Briefly, it seems that there is an inconsistency between the generalized entropy relation, Friedmann equation and the unified first law of thermodynamics.…”

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“…Now, for a theory in which S A = S A (A), since the Cai-Kim temperature meets the [9,10,15,16], one reaches…”

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Implications, Consequences and Interpretations of Generalized Entropy in the Cosmological Setups

Moradpour

2016

Int J Theor Phys

124

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Recently, it was argued (Eur. Phys. J. C 73, 2487 (2013)) that the total entropy of a gravitational system should be related to the volume of system instead of the system surface. Here, we show that this new proposal cannot satisfy the unified first law of thermodynamics and the Friedmans equation simultaneously, unless the effects of dark energy candidate on the horizon entropy are considered.In fact, our study shows that some types of dark energy candidate may admit this proposal. Some general properties of required dark energy are also addressed. Moreover, our investigation shows that this new proposal for entropy, while combined with the second law of thermodynamics (as the backbone of Verlinde's proposal), helps us in providing a thermodynamic interpretation for the difference between the surface and bulk degrees of freedom which, according to Padmanabhan's proposal, leads to the emergence of spacetime and thus the universe expansion. In fact, our investigation shows that the entropy changes of system may be equal to the difference between the surface and bulk degrees of freedom falling from surface into the system volume. Briefly, our results signal us that this new proposal for entropy may be in agreement with the thermodynamics laws,

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“…It has been argued in Refs. [35,36] that GSL confirms particular connection between thermodynamics, gravitation, and quantum theory; therefore, GSL has been studied extensively for both black holes and cosmological spacetimes [37][38][39][40]. Eventually, in this section we investigate the validity conditions of GSL at the apparent horizon of McVittie universe.…”

Section: Generalized Second Law Of Thermodynamicsmentioning

confidence: 96%

Generalized second law and universal relations of cosmological black hole

2019

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The objective of this paper is to investigate the validity conditions for the generalized second law of thermodynamics, and the universal relations for multi-horizon dynamical spacetime. It is found that there are three horizons of McVittie universe termed as event horizon, cosmological apparent horizon, and virtual horizon. The mass-dependent and mass-independent area product relations are formulated in terms of areas of the dynamical event horizon, cosmological horizon and virtual horizon. It is noted that whereas the area sum relation is mass independent, the area product relation is explicitly mass dependent. Moreover, we have also analyzed and listed explicit mass-independent and mass-dependent relations. Mathematics Subject Classification 83F05 IntroductionIn recent times, considerable interest has been shown in exploring universal relations constructed from the area product and sum relations of multi-horizon stationary black holes in super gravity, Einstein gravity and other modified theories of gravity [1][2][3][4][5][6]. In most cases, whereas the area product and sum relations are mass independent, they depend on various black hole parameters including charge, angular momentum, and cosmological constant. However, in some cases such as asymptotically non-flat spacetime, these relations fail to execute mass-independent relations [7-10]. Visser [11] found that the mass-independent area product relations fail in Schwarzschild-de Sitter black hole even if the contributions of the virtual horizon is included.Several authors [12][13][14] argued that the contribution of virtual horizon area should be added to build up mass-independent area-product and sum relations. However, in some cases, such contributions of virtual horizon could not sustain significantly [11]. It is known that a class of black holes admits more than one horizons, such as black hole event horizon (outer horizon), cauchy horizon (inner horizon), and virtual horizon (un-physical horizon). It has been argued [15][16][17][18] that like event horizon, other horizons are also associated with the notion of temperature and entropy. An extension of these notions has also been made for dynamical apparent horizon of FRW universe [19][20][21][22][23][24][25][26][27][28]. Despite the multiple horizons of stationary black holes, there are dynamical spacetime metrics containing dynamic multiple horizons.

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Apparent horizon and gravitational thermodynamics of the Universe: Solutions to the temperature and entropy confusions and extensions to modified gravity

Cited by 35 publications

References 120 publications

Entropy of a box of gas in an external gravitational field revisited

Entropy of a box of gas in an external gravitational field revisited

Implications, Consequences and Interpretations of Generalized Entropy in the Cosmological Setups

Generalized second law and universal relations of cosmological black hole

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