117 research outputs found
Generalized entropies and corresponding holographic dark energy models
Using Tsallis statistics and its relation with Boltzmann entropy, the Tsallis
entropy content of black holes is achieved, a result in full agreement with a
recent study (Phys. Lett. B 794, 24 (2019)). In addition, employing Kaniadakis
statistics and its relation with that of Tsallis, the Kaniadakis entropy of
black holes is obtained. The Sharma-Mittal and R\'{e}nyi entropy contents of
black holes are also addressed by employing their relations with Tsallis
entropy. Thereinafter, relying on the holographic dark energy hypothesis and
the obtained entropies, two new holographic dark energy models are introduced
and their implications on the dynamics of a flat FRW universe are studied when
there is also a pressureless fluid in background. In our setup, the apparent
horizon is considered as the IR cutoff, and there is not any mutual interaction
between the cosmic fluids. The results indicate that the obtained cosmological
models have ) notable powers to describe the cosmic evolution from the
matter-dominated era to the current accelerating universe, and ) suitable
predictions for the universe age
The extended uncertainty principle inspires the R\'{e}nyi entropy
We use the extended uncertainty principle (EUP) in order to obtain the
R\'{e}nyi entropy for a black hole (BH). The result implies that the
non-extensivity parameter, appeared in the R\'{e}nyi entropy formalism, may be
evaluated from the considerations which lead to EUP. It is also shown that, for
excited BHs, the R\'{e}nyi entropy is a function of the BH principal quantum
number, i.e. the BH quantum excited state. Temperature and heat capacity of the
excited BHs are also investigated addressing two phases while only one of them
can be stable. At this situation, whereas entropy is vanished, temperature may
take a non-zero positive minimum value, depending on the value of the
non-extensivity parameter. The evaporation time of excited BH has also been
studied
Tsallis uncertainty
It has been recently shown that the Bekenstein entropy bound is not respected
by the systems satisfying modified forms of Heisenberg uncertainty principle
(HUP) including the generalized and extended uncertainty principles, or even
their combinations. On the other, the use of generalized entropies, which
differ from Bekenstein entropy, in describing gravity and related topics
signals us to different equipartition expressions compared to the usual one. In
that way, The mathematical form of an equipartition theorem can be related to
the algebraic expression of a particular entropy, different from the standard
Bekenstein entropy, initially chosen to describe the black hole event horizon,
see E. M. C. Abreu et al., MPLA 32, 2050266 (2020). Motivated by these works,
we address three new uncertainty principles leading to recently introduced
generalized entropies. In addition, the corresponding energy-time uncertainty
relations and Unruh temperatures are also calculated. As a result, it seems
that systems described by generalized entropies, such as those of Tsallis, do
not necessarily meet HUP and may satisfy modified forms of HUP.Comment: Accepted version by EP
Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
We study the gravitational collapse of a homogeneous scalar field, minimally
coupled to gravity, in the presence of a particular type of dynamical
deformation between the canonical momenta of the scale factor and of the scalar
field. In the absence of such a deformation, a class of solutions can be found
in the literature [R. Goswami and P. S. Joshi, arXiv:gr-qc/0410144],
%\cite{JG04}, whereby a curvature singularity occurs at the collapse end state,
which can be either hidden behind a horizon or be visible to external
observers. However, when the phase-space is deformed, as implemented herein
this paper, we find that the singularity may be either removed or instead,
attained faster. More precisely, for negative values of the deformation
parameter, we identify the emergence of a negative pressure term, which slows
down the collapse so that the singularity is replaced with a bounce. In this
respect, the formation of a dynamical horizon can be avoided depending on the
suitable choice of the boundary surface of the star. Whereas for positive
values, the pressure that originates from the deformation effects assists the
collapse toward the singularity formation. In this case, since the collapse
speed is unbounded, the condition on the horizon formation is always satisfied
and furthermore the dynamical horizon develops earlier than when the
phase-space deformations are absent. These results are obtained by means of a
thoroughly numerical discussion.Comment: 17 pages, 17 figure
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