Schwarzschild black hole and generalized second law in phantom-dominated universe
Introduction
Astrophysical data show that the universe is accelerating [2]. Based on some data, it is possible to consider an evolving equation of state parameter, ω, less than −1 at present time from in the near past [3]. In this view we may assume that the universe is filled with a perfect fluid with a negative pressure and , dubbed as phantom dark energy [4]. A candidate for phantom dark energy is a phantom scalar field with wrong sign for kinetic energy term [5]. Another method to study the present inflation is to use a running cosmological constant based on principles of quantum field theory (specially on the renormalization group) which can mimic the phantom like behavior of the universe [6].
This description of the universe may contain finite time future singularity accompanied with dark energy density singularity called big rip. The big rip may be avoided by the effect of gravitational backreactions which can end the phantom-dominated regime [7]. We can consider horizons for the accelerating universe and associate entropy (as a measure of our ignorance about what is going behind it) and temperature to them [8], [9], [10], [11], [12], [13], [14]. In this way one is able to study the thermodynamics of a system consisting of dark energy perfect fluid and the horizon.
In phantom-dominated universe black holes lose their masses by accreting phantom fluid [16]. Therefore their areas and consequently their entropies will decrease. So it may be of interest to know that if the generalized second law of thermodynamics (GSL) is satisfied in this situation. Indeed if the thermodynamics parameters assigned to the universe are the same as the ordinary thermodynamics parameters known in physical systems, then one expects that thermodynamics laws be also satisfied for the universe.
Thermodynamics of an accelerating universe has been studied in several papers [17]. In [8] and [9], the generalized second law for cosmological models that depart slightly from de Sitter space and also when the horizon shrinks, was studied respectively. The thermodynamics of super-accelerated universe in a de Sitter and quasi-de Sitter space–time was the subject of the paper [10].
In [11], it was shown that for a phantom-dominated universe with constant ω the total entropy is a constant and for time dependent ω, via two specific examples, the validity of GSL was verified. In [12] the conditions of validity of GSL in more general cases, including the transition epoch (from quintessence to phantom), and for temperatures proportional to de Sitter temperature were studied independently of the origin of dark energy.
In a recent paper the author of [1], using phantom scalar field model, showed that GSL is violated in the presence of a Schwarzschild black hole in the cases studied in [11] and in phantom-dominated era. In this Letter we try to study the same problem but by considering a temperature other than de Sitter temperature. Our study is independent of the origin of phantom like behavior of the universe. We also consider the possibility of transition from quintessence to phantom regime and discuss the validity of GSL in the neighborhood of transition time in the presence of the black hole.
We use the units .
Section snippets
GSL in the phantom-dominated FRW universe in the presence of a Schwarzschild black hole
We consider spatially flat Friedman–Robertson–Walker (FRW) metric with scale factor : The Hubble parameter is given by . The overdot shows derivative with respect to the comoving time t. The equation of state of the universe which is assumed to behave as a perfect fluid at large scale is given by where ω is the equation of state parameter. For an accelerating universe, i.e. , we have . The future event horizon, , is given by
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2022, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy PhysicsCitation Excerpt :One of the most pivotal discoveries of the last decades is that the universe is accelerating [1]. Considering thermal properties of an accelerated universe [2], the investigation of the generalized second law (GSL) defining black holes (BHs) thermodynamics has increased [3]. Namely, there exist theoretical proofs concerning the thermodynamical features of BH.
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