arXiv subjects

Shin'ichi Nojiri

Publications and source records attributed to Shin'ichi Nojiri.

At least 73 records · Page 4Linked to original sources

arXiv2022

New entropies, black holes, and holographic dark energy

The Bekenstein-Hawking entropy is a cornerstone of horizon thermodynamics but quantum effects correct it, while inequivalent entropies arise also in non-extensive thermodynamics. Reviewing our previous work, we advocate for a new entropy construct that comprises recent and older proposals and satisfies four minimal key properties. The new proposal is then applied to black holes and to holographic dark energy and shown to have the potential to cause early universe inflation or to alleviate the current Hubble tension. We then analyze black hole temperatures and masses consistent with alternative entropies.

gr-qc↗

arXiv2022

Multi-horizons black hole solutions, photon sphere and perihelion shift in weak ghost-free Gauss-Bonnet theory of gravity

Among the modified gravitational theories, the ghost-free Gauss-Bonnet (GFGB) theory of gravity has been considered from the viewpoint of cosmology. The best way to check its applicability could be to elicit observable predicts which give guidelines or limitations on the theory, which could be contrasted with the actual observations. In the present study, we derive consistent field equations for GFGB and by applying the equations to a spherically symmetric space-time, we obtain new spherically symmetric black hole (BH) solutions. We study the physical properties of these BH solutions and show that the obtained space-time possesses multi-horizons and the Gauss-Bonnet invariants in the space-time are not trivial. We also investigate the thermodynamical quantities related to these BH solutions and we show that these quantities are consistent with what is known in the previous works. Finally, we study the geodesic equations of these solutions which give the photon spheres and we find the perihelion shift for weak GFGB. In addition, we calculate the first-order GFGB perturbations in the Schwarzschild solution and new BH solutions and show that we improve and extend existing results in the past literature on the spherically symmetric solutions.

gr-qc↗

arXiv2022

Alternative entropies and consistent black hole thermodynamics

While the Bekenstein-Hawking entropy is the unique notion of entropy that makes classical black hole thermodynamics consistent, alternative entropy notions (Rényi, Tsallis, and generalized constructs) abound in the literature. We explore conditions under which they are part of a consistent horizon thermodynamics for certain classes of modified gravity black holes. We provide examples in which black hole masses and temperatures going hand-in-hand with these alternative entropies coincide with their usual counterparts associated with the Bekenstein-Hawking entropy.

gr-qc↗

arXiv2022

Early and late universe holographic cosmology from a new generalized entropy

We propose a new four-parameter entropy function that generalizes the Tsallis, Rényi, Barrow, Sharma-Mittal, Kaniadakis and Loop Quantum Gravity entropies for suitable limits of the parameters. Consequently, we address the early and late universe cosmology corresponding to the proposed four-parameter entropy function. As a result, it turns out that the entropic cosmology from the generalized entropy function can unify the early inflation to the late dark energy era of the universe. In such a unified scenario, we find that -- (1) the inflation era is described by a quasi de-Sitter evolution of the Hubble parameter, which has an exit at around 58 e-folding number, (2) the inflationary observable quantities like the spectral index for primordial scalar perturbation and the tensor-to-scalar ratio are simultaneously compatible with the recent Planck data, and (3) regarding the late time cosmology, the dark energy EoS parameter is found to be consistent with the Planck result for the same values of the entropy parameters that lead to the viable inflation during the early universe. Furthermore, we show that the entropic cosmology from the proposed entropy function is equivalent to holographic cosmology, where the respective holographic cut-offs are determined in terms of either particle horizon and its derivative or future horizon and its derivative.

gr-qc↗

arXiv2022

Black holes with Lagrange multiplier and potential in mimetic-like gravitational theory: multi-horizon black holes

In this paper, we employ the {\bf mimetic-like} field equations coupled with the Lagrange multiplier and %mimetic {\bf potential} to derive non-trivial spherically symmetric black hole (BH) solutions. We divided this study into three cases: The first one in which we take the Lagrange multiplier and %mimetic {\bf the potential} to have vanishing value and derive a BH solution that completely coincides with the BH of the Einstein general relativity despite the non-vanishing value of the {\bf mimetic-like scalar field}. The first case is completely consistent with the previous studies in the literature that mimetic theory coincides with GR \cite{Nashed:2018qag}. In the second case, we derive a solution with a constant value of the {\bf potential} and a dynamical value of the Lagrange multiplier. This solution has no horizon and therefore the obtained spacetime does not correspond to the BH. In this solution, there appears the region of the Euclidian signature where the signature of the diagonal components of the metric is $(+,+,+,+)$ or the region with two times where the signature is $(+,+,-,-)$. Finally, we derive a BH solution with non-vanishing values of the Lagrange multiplier, {\bf potential}, and {\bf mimetic-like scalar field}. This BH shows a soft singularity compared with the Einstein BH solution. The relevant physics of the third case is discussed by showing their behavior of the metric potential at infinity, calculating their energy conditions, and study their thermodynamical quantities. We give a brief discussion on how our third case can generate a BH with three horizons as in the de Sitter-Reissner-Nordström black hole spacetime, where the largest horizon is the cosmological one and two correspond to the outer and inner horizons of the BH. Even in the third case, there appears the region of the Euclidian signature or the region with two times.

gr-qc↗

arXiv2022

Consistency between black hole and mimetic gravity -- Case of $(2+1)$-dimensional gravity

We show that the mimetic theory with the constraint $g^{ρσ}\partial_ρϕ\partial_σϕ=1$ cannot realize the black hole geometry with the horizon(s). To overcome such issue, we may change the mimetic constraint a little bit by $ω(ϕ) g^{ρσ}\partial_ρϕ\partial_σϕ=-1,$ where $ω(ϕ)$ is a function of the scalar field $ϕ$. As an example, we consider $(2+1)$-dimensional mimetic gravity with the mimetic potential and construct black hole (BH) solutions by using this modified constraint. We study three different classes: In the first class, we assume the Lagrange multiplier and mimetic potential are vanishing and obtain a BH solution that fully matches the BH of GR despite the non-triviality of the mimetic field which ensures the study presented in {\it JCAP 01 (2019) 058}. In the second class, we obtain a BH having constant mimetic potential and a non-trivial form of the Lagrange multiplier. In the third class, we obtain a new BH solution with non-vanishing values of the mimetic field, the Lagrange multiplier, and the mimetic potential. In any case, the solutions correspond to the space-time with only one horizon but we show that the formalism for the constraint works.

gr-qc↗

arXiv2022

Towards a smooth unification from an ekpyrotic bounce to the dark energy era

In the context of a ghost free $f(R,\mathcal{G})$ model, we present a non-singular cosmological scenario in which the universe initially contracts through an ekpyrotic phase having a bouncing like behaviour, and following the bounce, it smoothly transits to a matter or radiation like deceleration era which is further smoothly connected to the dark energy era at present epoch. We consider the Gauss-Bonnet (GB) coupling function in such a way that it gets compatible with the event GW170817. Using suitable reconstruction technique, we obtain the non-trivial scalar field potential as well as the GB coupling function. Such scalar potential and GB coupling function source a smooth unified scenario from an ekpyrotic bounce to the dark energy era with an intermediate deceleration era. The occurrence of ekpyrotic contraction phase justifies the resolution of the anisotropic problem (also known as BKL instability) in the background evolution. The Hubble radius shows an asymmetric behaviour around the bounce, in particular, the evolution of the Hubble radius leads to the generation era of the primordial perturbation modes far before the bounce in the deep sub-Hubble regime. Accordingly we perform the scalar and tensor perturbation evolution in the present context, and as a result, the scalar power spectrum at large scale modes is found to be problematic. Thus an extended scenario is proposed where we consider a pre-ekpyrotic phase having the equation of state parameter is less than unity, and re-examine the scalar and tensor power spectra, on large scales that cross the Hubble radius during the pre-ekpyrotic stage. In this regard, the GB coupling function shows considerable effects in reducing the tensor to scalar ratio compared to the case where the GB coupling is absent. Furthermore the dark energy epoch is consistent with the Planck+SNe+BAO data.

gr-qc↗

arXiv2022

How fundamental is entropy? From non-extensive statistics and black hole physics to the holographic dark universe

We propose a new entropy construct that generalizes the Tsallis, Rényi, Sharma-Mittal, Barrow, Kaniadakis, and Loop Quantum Gravity entropies and reduces to the Bekenstein-Hawking entropy in a certain limit. This proposal is applied to the Schwarzschild black hole and to spatially homogeneous and isotropic cosmology, where it is shown that it can potentially describe inflation and/or holographic dark energy.

gr-qc↗

arXiv2021

Specific neutral and charged black holes in $f(R)$ gravitational theory

With the successes of $f(R)$ theory as a neutral modification of Einstein's general relativity (GR), we continue our study in this field and attempt to find general %natural { neutral} and charged black hole (BH) solutions. In the previous papers \cite{Nashed:2020mnp,Nashed:2020tbp}, we applied the field equation of the $f(R)$ gravity to a spherically symmetric space-time $ds^2=-U(r)dt^2+\frac{dr^2}{V(r)}+r^2 \left( dθ^2+\sin^2θdϕ^2 \right)$ with unequal metric potentials $U(r)$ and $V(r)$ and with/without electric charge. {Then we have obtained equations which include all the possible static solutions with spherical symmetry.} To ensure the closed form of system of the resulting differential equations in order to obtain specific solutions, we assumed the derivative of the $f(R)$ with respect to the scalar curvature $R$ to have a form %$F_1(r)=\frac{df(R(r))}{dR(r)} \propto %{\color{red} 1 +} %\frac{c}{r^n}$ but in case $n>2$, the resulting black hole solutions with/without charge do not %generate asymptotically GR BH solutions in the limit $c\rightarrow 0$ which means that the only case that can generate GR BHs is $n=2$. %In this paper, we assume another form, i.e., $F_1(r) {=\frac{df(R(r))}{dR(r)} } = 1-\frac{F_0-\left(n-3\right)}{r^n}$ with a constant $F_0$ and show that we can generate asymptotically GR BH solutions for $n>2$ but we show that the $n=2$ case is not allowed. This form of $F_1(r)$ could be the most acceptable physical form that we can generate from it physical metric potentials that can have a well-known asymptotic form and we obtain the metric of the Einstein general relativity in the limit of $F_0\to n-3$. We show that the form of the electric charge depends on $n$ and that $n\neq 2$.}

gr-qc↗

arXiv2021

Barrow entropic dark energy: A member of generalized holographic dark energy family

The holographic cut-off, in the formalism of generalized holographic dark energy (HDE), is generalized to depend on $L_\mathrm{IR} = L_\mathrm{IR} \left( L_\mathrm{p}, \dot L_\mathrm{p}, \ddot L_\mathrm{p}, \cdots, L_\mathrm{f}, \dot L_\mathrm{f}, \cdots, a\right)$, where $L_\mathrm{p}$ and $L_\mathrm{f}$ are the particle horizon and future horizon respectively, and $a$ is the scale factor of the universe. Based on such formalism, we showed that the Barrow entropic dark energy (DE) model is equivalent to the generalized HDE where the respective holographic cut-off is determined by two ways -- (1) in terms of particle horizon and its derivative and (2) in terms of future horizon and its derivative. Interestingly, such cut-off turns out to depend up-to first order derivative of $L_\mathrm{p}$ or $L_\mathrm{f}$ respectively. Such equivalence between the Barrow entropic dark energy and the generalized HDE is extended to the scenario where the exponent of the Barrow entropy allows to vary with the cosmological expansion of the universe. In both the cases (whether the Barrow exponent is a constant or varies with the cosmological evolution), we determine effective equation of state (EoS) parameter from the generalized holographic point of view, which, by comparing with the Barrow DE EoS parameter, further ensures the equivalence between the Barrow entropic dark energy and the generalized HDE.

gr-qc↗

arXiv2021

Two Dimensional Conformal Field Theory from Soft Quantum Electrodynamics in Four Dimensions

In this work, we propose an effective action of the two-dimensional conformal field theory for the Soft modes appearing in Quantum ElectroDynamics (QED) in 4 dimensions. This is motivated in two ways. First, we motivate the notion of an effective action for the Soft modes using the path integral formalism. Second, by noting the transformations of the on-shell gauge-fixed QED action, we deduce necessary boundary conditions and the corresponding form of the counter-terms that govern the IR sector. We review a derivation of the Soft Ward-Takahashi identity using path integral methods and offer an alternative derivation that follows from the large-gauge variations of the QED action. Because our effective action is that of a conformal theory, we calculate the relevant central charge.

hep-th↗

arXiv2021

Rotating black hole in $f(R)$ theory

In general, the field equation of $f(R)$ gravitational theory is very intricate, and therefore, it is not an easy task to derive analytical solutions. We consider rotating black hole spacetime four-dimensional in the $f(R)$ gravitational theory and derive a novel black hole solution. This black hole reduced to the one presented in \cite{Nashed:2020mnp} when the rotation parameter, $Ω$, vanishes. We study the physical properties of this black hole by writing its line element and show that it asymptotically behaves as the AdS/dS spacetime. Moreover, we derive the values of various invariants finding that they do possess the central singularity, and show that our black hole has a strong singularity compared with the black hole of the Einstein general relativity (GR). We calculate several thermodynamical quantities and show that we have two horizons, the inner and outer Cauchy horizons in contrast to GR. From the calculations of thermodynamics, we show that the outer Cauchy horizon gives satisfactory results for the Hawking temperature, entropy, and quasi-local energy. Moreover, we show that our black hole has a positive value of the Gibbs free energy which means that it is a stable one. Finally, we derive the stability condition analytically and graphically using the geodesic deviation method.

gr-qc↗

arXiv2021

Area-law versus Rényi and Tsallis black hole entropies

The Rényi and Tsallis entropies are discussed as possible alternatives to the Bekenstein-Hawking area-law entropy. It is pointed out how replacing the entropy notion, but not the Hawking temperature and the thermodynamical energy may render the whole black hole thermodynamics inconsistent. The possibility to relate the Rényi and Tsallis entropies with the quantum gravity corrected Bekenstein-Hawking entropy is discussed.

gr-qc↗

arXiv2021

Dressed-Asymptotic States and QED Infrared Physics

The dressed state formalisms, which incorporate interactions of soft particles into an asymptotic state, are known as the prescriptions expected to solve the problem of infrared (IR) divergence in the quantum field theory (QFT). A particularly famous example is the dressed state formalism proposed by Kulish and Faddeev in quantum electrodynamics (QED). As pointed out by Hirai and Sugishita, however, this formalism has problems in gauge invariance and the IR divergence. These problems are mainly caused by the existence of ghosts or unphysical photon modes. Therefore, we start by studying the asymptotic states in the Coulomb gauge, which excludes ghosts and/or unphysical photon modes. In this paper, we propose a formalism to construct the asymptotic states directly from the interaction of the theory by setting a sufficiently large time scale $T$. In this dressed state formalism, we define the asymptotic interaction remaining at $|t|>T$ in terms of some fixed order of $1/T$, and we are performing all calculations according to that order. We study the asymptotic states in QED specifically, but we can formally apply the dressed state formalism proposed in this paper to any perturbative QFT. We show that, at least in QED, we can construct divergence-free and unitary $S$-matrix using dressed states proposed in this paper. Furthermore, we discuss the transition rate to show that we can predict experimental results. We also show that the $\mathrm{U}(1)$ gauge symmetry of $S$-matrix leads to the QED large gauge symmetry, and deviation of the expectation values of the vector potential between initial and final spacelike hypersurfaces emerges as a QED memory effect. The dressed state formalism in this paper may give a unified and new insight into IR physics, including asymptotic symmetries, memory effects, and unitarity of the state evolution.

hep-th↗

arXiv2021

Thermal effects and scalar modes in the cosmological propagation of gravitational waves

We consider thermal effects in the propagation of gravitational waves on a cosmological background. In particular, we consider scalar field cosmologies and study gravitational modes near cosmological singularities. We point out that the contribution of thermal radiation can heavily affect the dynamics of gravitational waves giving enhancement or dissipation effects both at quantum and classical level.These effects are considered both in General Relativity and in modified theories like $F(R)$ gravity which can be easily reduced to scalar-tensor cosmology. The possible detection and disentanglement of standard and scalar gravitational modes on the stochastic background are also discussed.

gr-qc↗

arXiv2021

Mimetic Euler-Heisenberg theory, charged solutions and multi-horizon black holes

We construct several new classes of black hole (BH) solutions in the context of the mimetic Euler-Heisenberg theory. We separately derive three differently charged BH solutions and their relevant mimetic forms. We show that the asymptotic form of all BH solutions behaves like a flat spacetime. These BHs, either with/without cosmological constant, have the non constant Ricci scalar, due to the contribution of the Euler-Heisenberg parameter, which means that they are not solution to standard or mimetic $f(R)$ gravitational theory without the Euler-Heisenberg non-linear electrodynamics and at the same time they are not equivalent to the solutions of the Einstein gravity with a massless scalar field. Moreover, we display that the effect of the Euler-Heisenberg theory makes the singularity of BH solutions stronger compared with that of BH solutions in general relativity. Furthermore, we show that the null and strong energy conditions of those BH solutions are violated, which is a general trend of mimetic gravitational theory. The thermodynamics of the BH solutions are satisfactory although there appears a negative Hawking temperature under some conditions. Additionally, these BHs obey the first law of thermodynamics. We also study the stability, using the geodesic deviation, and derive the stability condition analytically and graphically. Finally, for the first time and under some conditions, we derived multi-horizon BH solutions in the context of the mimetic Euler-Heisenberg theory and study their related physics.

gr-qc↗

arXiv2021

Analytic charged BHs in $f(\mathcal{R})$ gravity

In this article, we seek exact charged spherically symmetric black holes (BHs) with considering $f(\mathcal{R})$ gravitational theory. These BHs are characterized by convolution and error functions. Those two functions depend on a constant of integration which is responsible to make such a solution deviate from the Einstein general relativity (GR). The error function which constitutes the charge potential of the Maxwell field depends on the constant of integration and when this constant is vanishing we can not reproduce the Reissner-Nordström BH in the lower order of $f(\mathcal{R})$. This means that we can not reproduce Reissner-Nordström BH in lower-order-curvature theory, i.e., in GR limit $f(\mathcal{R})=\mathcal{R}$, we can not get the well known charged BH. We study the physical properties of these BHs and show that it is asymptotically approached as a flat spacetime or approach AdS/dS spacetime. Also, we calculate the invariants of the BHS and show that the singularities are milder than those of BH's of GR. Additionally, we derive the stability condition through the use of geodesic deviation. Moreover, we study the thermodynamics of our BH and investigate the impact of the higher-order-curvature theory. Finally, we show that all the BHs are stable and have radial speed equal to one through the use of odd-type mode.

hep-th↗

arXiv2021

Statistical System based on $p$-adic numbers

We propose statistical systems based on $p$-adic numbers. In the systems, the Hamiltonian is a standard real number which is given by a map from the $p$-adic numbers. Therefore we can introduce the temperature as a real number and calculate the thermodynamical quantities like free energy, thermodynamical energy, entropy, specific heat, etc. Although we consider a very simple system, which corresponds to a free particle moving in one dimensional space, we find that there appear the behaviors like phase transition in the system. Usually in order that a phase transition occurs, we need a system with an infinite number of degrees of freedom but in the system where the dynamical variable is given by $p$-adic number, even if the degree of the freedom is unity, there might occur the phase transition.

cond-mat.stat-mech↗