Assuming the hypothesis of the entropic nature of gravity, we calculate generalized Newtonian forces, their associated potentials and field equations, when other, in general non-extensive, entropies are considered instead of the usual Boltzmann entropy. Some comments about the nature of the correction terms presented are given, and a calculation of corrections to the Bekenstein-Hawking temperature is performed using the arguments which lead to what can be called a Michell-Laplace black hole.
Newtonian gravitation with some slight modifications, along with some highly simplified ideas from quantum field theory allow us to reproduce, at least at the level of back-of-the-envelope calculations, many results of black hole physics. We consider particle production by a black hole, the Newtonian equivalent of the Hawking temperature, and the Bekenstein entropy. Also, we are able to deduce Newtonian field equations from entropy. We finally study higher-order Newtonian theories under the same assumptions used for ordinary Newtonian theory. In a companion article we will look at entropic for…
We consider the particle creation scenario in the dynamical Chern-Simons modified gravity in the presence of perfect fluid equation of state $p=(γ-1)ρ$. By assuming various modified entropies (Bekenstein, logarithmic, power law correction and Reyni), we investigate the first law of thermodynamics and generalized second law of thermodynamics on the apparent horizon. In the presence of particle creation rate, we discuss the generalized second law of thermodynamics and thermal equilibrium condition. It is found that thermodynamic laws and equilibrium condition remain valid under certain condition…
Here we make an attempt to extend the idea of generalized Hawking temperature and modified Bekenstein entropy at the event horizon in a fractal universe. The modified Hawking temperature and Bekenstein entropy are considered in the governing Friedmann equations, which is modified in the background of a fractal universe. The validity of the Generalized second law of thermodynamics\,(GSLT) and Thermodynamic Equilibrium\,(TE) have been examined and compared graphically in a fractal universe filled with a perfect fluid having the constant equation of state in three different generalized Bekenstein…
The recently proposed Nieh-Yan modified teleparallel gravity is a parity-violating gravity model that modifies the general relativity equivalent teleparallel gravity by a Nieh-Yan term. This model is healthy and simple in form. In this paper, we consider the application of this model to the Solar System and investigate its slow-motion and weak-field approximation in terms of the parametrized post-Newtonian formalism. We find that all the post-Newtonian parameters of the model are the same as those of general relativity, which makes the model compatible with the Solar System experiments.
Topological and optical signatures of modified black-hole entropies
Indian Institute of Technology, Kanpur（坎普尔印度理工学院）；State University of Tetovo（泰托沃国立大学）；National Observatory of Athens（雅典国家天文台）；Academy of Athens, Research Center for Astronomy and Applied Mathematics（雅典科学院天文学与应用数学研究中心）；School of Sciences, European University Cyprus（塞浦路斯欧洲大学理学院）；Universidad Católica del Norte（北天主教大学）；CAS Key Laboratory for Researches in Galaxies and Cosmology, School of Astronomy and Space Science, University of Science and Technology of China（中国科学院星系与宇宙学重点实验室，中国科学技术大学天文与空间科学学院）
Indian Institute of Technology, Kanpur（坎普尔印度理工学院）；Central University of Himachal Pradesh（喜马偕尔邦中央大学）；State University of Tetovo（泰托沃国立大学）；National Observatory of Athens（雅典国家天文台）；Universidad Católica del Norte（北天主教大学）；University of Science and Technology of China（中国科学技术大学）
The proposed Satellite Test of the Equivalence Principle (STEP) will detect possible violations of the Weak Equivalence Principle by measuring relative accelerations between test masses of different composition with a precision of one part in $10^{18}$. A serendipitous byproduct of the experimental design is that the absolute (common-mode) acceleration of the test masses is also measured to high precision as they oscillate along a common axis under the influence of restoring forces produced by the position sensor currents, which in drag-free mode lead to Newtonian accelerations as small as $10…
In this paper, we analyze the clustering of galaxies using a modified theory of gravity, in which the field content of general relativity has been be increased. This increasing in the field content of general relativity changes the large distance behavior of the theory, and in weak field approximation, it will also modify the large distance behavior of Newtonian potential. So, we will analyzing the clustering of multi-component system of galaxies interacting through this modified Newtonian potential. We will obtain the partition function for this multi-component system, and study the thermodyn…
The Heisenberg uncertainty principle is known to be connected to the entropic uncertainty principle. This correspondence is obtained employing a Gaussian probability distribution for wave functions associated to the Shannon entropy. Independently, due to quantum gravity effects the Heisenberg uncertainty principle has been extended to a Generalized Uncertainty Principle (GUP). In this work, we show that GUP has been derived from considering non-extensive entropies, proposed by one of us. We found that the deformation parameters associated with $S_{+}$ and $S_-$ entropies are negative and posit…
We derive from first principles third post-Newtonian (3PN) accurate Keplerian-type parametric solution to describe PN-accurate dynamics of non-spinning compact binaries in hyperbolic orbits. Orbital elements and functions of the parametric solution are obtained in terms of the conserved orbital energy and angular momentum in both Arnowitt-Deser-Misner type and modified harmonic coordinates. Elegant checks are provided that include a modified analytic continuation prescription to obtain our independent hyperbolic parametric solution from its eccentric version. A prescription to model gravitatio…
We have found some analytical cosmological solutions to MOdified Gravity (MOG). These solutions describe different evolutionary epochs of an isotropic and homogeneous universe. During each epoch, the evolution of cosmological perturbation is studied in the Newtonian framework and compared with the corresponding results of GR.
Modified Newtonian dynamics by Milgrom is a paradigm for explaining the rotation curves of spiral galaxies and various other large scale structures. This paradigm includes several different theories. Here we present Milgrom's modified inertia (MI) theory in terms of a simple and tractable non-conservative Newtonian dynamics, which is useful in obtaining observable predictions of MI. It is found that: 1) Modified inertia theory is equivalent to a Newtonian theory, with a non-conservative gravitational field, and dark matter density; 2) The tidal force in the equivalent Newtonian dynamics is non…
We compare six models (including the baryonic model, two dark matter models, two modified Newtonian dynamics models and one modified gravity model) in accounting for the galaxy rotation curves. For the dark matter models, we assume NFW profile and core-modified profile for the dark halo, respectively. For the modified Newtonian dynamics models, we discuss Milgrom's MOND theory with two different interpolation functions, i.e. the standard and the simple interpolation functions. As for the modified gravity, we focus on Moffat's MSTG theory. We fit these models to the observed rotation curves of …
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 fro…
We study the statistical mechanics of binary systems under gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems, in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of physical parameters…
In this paper we have shown that the connection between the number of bits and the area of the holographic screen, where both were established in Verlinde's theory of entropic gravity, may depend on the thermostatistics theory previously chosen. Starting from the Boltzmann-Gibbs (BG) theory, we have reobtained the usual dependency of both, bits number and area. After that, using Tsallis' entropy concept within the entropic gravity formalism, we have derived another relation between the bits number and the holographic screen area. Moreover, we have used this new relation to derive three Newtoni…
The idea of possible modification to gravity theory, whether it is in the Newtonian or general relativistic premises, is there for quite sometime. Based on it, astrophysical and cosmological problems are targeted to solve. But none of the Newtonian theories of modification has been performed from the first principle. Here, we modify Poisson's equation and propose two possible ways to modify the law gravitation which, however, reduces to Newton's law far away from the center of source. Based on these modified Newton's laws, we attempt to solve problems lying with white dwarfs. There are observa…
A reformulation of the Schwarzschild solution of the linearised Einstein field equations in post-Riemannian Finsler spacetime is derived. The solution is constructed in three stages: the exterior solution, the event-horizon solution and the interior solution. It is shown that the exterior solution is asymptotically similar to Newtonian gravity at large distances implying that Newtonian gravity is a low energy approximation of the solution. Application of Eddington-Finklestein coordinates is shown to reproduce the results obtained from standard general relativity at the event horizon. Further a…
We study the thermodynamics of galaxy clusters in a modified Newtonian potential motivated by a general solution to Newton's "sphere-point" equivalence theorem. We obtain the $N$ particle partition function by evaluating the configurational integral while accounting for the extended nature of galaxies (via the inclusion of the softening parameter $ε$ into the potential energy function). This softening parameter takes care of the galaxy-halos whose effect on structuring the shape of the galactic disc has been found recently. The spatial distribution of the particles (galaxies) is also studied i…
The growing availability of increasingly accurate data on transiting exoplanets suggests the possibility of using these systems as possible testbeds for modified models of gravity. In particular, we suggest that the post-Keplerian (pK) dynamical effects from the perturbations of the Newtonian potential falling off as the square or the cube of the distance from the mass of the host star break the degeneracy of the anomalistic, draconitic and sidereal periods. The latter are characteristic temporal intervals in the motion of a binary system, and all coincide in the purely Keplerian case. We work…
Recent experimental results for the gravitational constant G from Cavendish-type experiments were analysed in the framework of Modified Newtonian Dynamics (MOND). MOND corrections were applied to the equation of motion of a pendulum, under the assumption that the magnitude of the horizontal time dependent gravitational acceleration determines the amount of MOND corrections. The large vertical component of the local gravitational field of the earth is fully compensated by the alignment of the torsion pendulum in accordance with Newtons third law and therefore not considered for MOND corrections…
We investigate the integrability conditions of a class of shear-free perfect-fluid cosmological models within the framework of anisotropic fluid sources, applying our results to f(R) dark energy models. Generalising earlier general relativistic results for time-like geodesics, we extend the potential and acceleration terms of the quasi-Newtonian formulation of integrable dust cosmological models about a linearized Friedmann-Lemaitre-Robertson-Walker background and derive the equations that describe their dynamical evolutions. We show that in general, models with an anisotropic fluid source are…
Based on Newtonian dynamics, observations show that the luminous masses of astrophysical objects that are the size of a galaxy or larger are not enough to generate the measured motions which they supposedly determine. This is typically attributed to the existence of dark matter, which possesses mass but does not radiate (or absorb radiation). Alternatively, the mismatch can be explained if the underlying dynamics is not Newtonian. Within this conceptual scheme, Modified Newtonian Dynamics (MOND) is a successful theoretical paradigm. MOND is usually expressed in terms of a nonlinear Poisson equ…
A generalization of Bekenstein's Tensor-Vector-Scalar (TeVeS) model of modified gravity has recently been proposed as an alternative to dark matter. This model -- which we will refer to as g-TeVeS -- utilizes a Galileon-induced Vainshtein mechanism to suppress modifications to General Relativity in strong gravity regimes and so avoids the need to introduce the baroque kinetic terms that typically exist in relativistic models of Modified Newtonian Dynamics (MOND). We explore the behavior of this model in spacetimes with exact Friedmann-Robertson-Walker (FRW) symmetry. The ability of the theory …
In the weak-field limit of General Relativity, gravitational waves obey linear equations and propagate at the speed of light. These properties of General Relativity are supported by the observation of ultra high energy cosmic rays as well as by LIGO's recent detection of gravitation waves. We argue that two existing relativistic generalizations of Modified Newtonian Dynamics, namely Generalized Einstein-Aether theory and BIMOND, display fatal inconsistencies with these observations.
The Newtonian gravitational constant $G$ obeys the dimensional relation $[G] [M] [a] = [v]^4$, where $M$, $a$, and $v$ denote mass, acceleration, and speed, respectively. Since the baryonic Tully-Fisher (BTF) and Faber-Jackson (BFJ) relations are observed facts, this relation implies that $G\, a = {\rm constant}$. This result cannot be obtained in Newtonian dynamics which cannot explain the origin of the BTF and BFJ relations. An alternative, modified Newtonian dynamics (MOND) assumes that $G=G_0$ is constant in space and derives naturally a characteristic constant acceleration $a=a_0$, as wel…
Galactic Sun's motion in the Cold Dark Matter, MOdified Newtonian Dynamics and MOdified Gravity scenarios
我们数值积分的太阳在银河系中心直角坐标系中的运动方程的-4.5 Gyr <= t <= 0的冷暗物质（CDM）晕的两种不同的模型，在修改的牛顿动力学（MOND）和修改的重力（MOG）没有诉诸CDM。所用的初始条件来自于对太阳在银河系（MW）中三维运动的最新运动学测定，即假设静止地方标准（LSR）的旋转速度为最近的值Θ_0=268 km s^-1，IAU推荐的值为Θ_0=220 km s^-1;假设太阳位于距离银河系中心（GC）8.5 kpc处。对于Θ_0=268 km/s^-1，太阳的诞生时间为4.5 Gyr前，应该发生在银河系中心距离很大的地方（12-27 kpc，取决于所用的模型），而对于Θ_0=220 km/s^-1，几乎所有的模型都认为太阳的诞生时间大约为8.8-9.3 kpc。积分后的轨道远不是圆形的，特别是在Θ_0=268 km s^-1的情况下，并且与CDM模型的结果不同，CDM模型得到的太阳轨道的空间扩展最广。
We estimate galaxy clustering under a modified gravitational potential. In particular, the modifications in gravitational potential energy occur due to a power-law and cosmological constant terms. We derive a canonical partition function for the system of galaxies interacting under such a modified gravitational potential. Moreover, we compute various thermodynamical equation of states for the system. We do comparative analysis in order to emphasize the effect of corrections on thermodynamics of the system. Interestingly, the modifications in thermodynamical quantities are embedded in clusterin…
Screened modified gravity (SMG) is a kind of scalar-tensor theories with screening mechanisms, which can generate screening effect to suppress the fifth force in high density environments and pass the solar system tests. Meanwhile, the potential of scalar field in the theories can drive the acceleration of the late universe. In this paper, we calculate the parameterized post-Newtonian (PPN) parameters $γ$ and $β$, the effective gravitational constant $G_{\rm eff}$ and the effective cosmological constant $Λ$ for SMG with a general potential $V$ and coupling function $A$. The dependence of these…
Two exact solutions for $n=0$ and $n=1$ of the Palatini-modified Lane-Emden equation are found. We have employed these solutions to describe a Palatini-Newtonian neutron star and compared the result with the pure Newtonian counterpart. It turned out that for the negative parameter of the Starobinsky model the star is heavier and larger.
We test a free {\it ad hoc} parametrization of the Tolman-Oppenheimer-Volkoff (TOV) equation. We do not have in mind any specific extended theory of gravity (ETG) but each new parameter introduced has a physical interpretation. Our aim is fully pedagogical rather than a proposal for a new ETG. Given a realistic neutron star equation of state we map the contributions of each new parameter into a shift in trajectories of the mass-radius diagram. This exercise allows us to make the correspondence between each TOV sector with possible modifications of gravity and clarifies how neutron star observa…
The Local Group (LG) is {an appropriate} test system for Modified Newtonian Dynamics, since the acceleration of M31 galaxy is fully in the deep MOND regime $a \ll a_0$. We model the LG as a two body problem of $M31$ and the Milky Way (MW) galaxies. {Extending previous studies, we also include the Cosmological Constant.} The assumption that in the big bang the galaxies emerged from the same place and approach to the measured distance and velocity today (the Timing Argument), predicts the total mass for the LG: $(0.447 \pm 0.005)\cdot 10^{12} M_{\odot}$. The corresponding motion of the LG predic…
