Higher-Dimensional Regular Reissner–Nordström Black Holes Associated with Linear Electrodynamics

Following the interpretation of matter source that the energy-momentum tensor of anisotropic fluid can be dealt with effectively as the energy-momentum tensor of perfect fluid plus linear (Maxwell) electromagnetic field, we obtain the regular higher-dimensional Reissner–Nordström (Tangherlini–RN) solution by starting with the noncommutative geometry-inspired Schwarzschild solution. Using the boundary conditions that connect the noncommutative Schwarzschild solution in the interior of the charged perfect fluid sphere to the Tangherlini–RN solution in the exterior of the sphere, we find that the interior structure can be reflected by an exterior parameter, the charge-to-mass ratio. Moreover, we investigate the stability of the boundary under mass perturbation and indicate that the new interpretation imposes a rigid restriction upon the charge-to-mass ratio. This restriction, in turn, permits a stable noncommutative black hole only in the 4-dimensional spacetime.

On the renormalization of entanglement entropy

The renormalization of entanglement entropy of quantum field theories is investigated in the simplest setting with a λϕ4 scalar field theory. The 3+1 dimensional spacetime is separated into two regions by an infinitely flat 2-dimensional interface. The entanglement entropy of the system across the interface has an elegant geometrical interpretation using the replica trick, which requires putting the field theory on a curved spacetime background. We demonstrate that the theory, and hence the entanglement entropy, is renormalizable at order λ once all the relevant operators up to dimension 4 are included in the action. This exercise has a one-to-one correspondence to entanglement entropy interpretation of the black hole entropy which suggests that our treatment is sensible. Our study suggests that entanglement entropy is renormalizable and is a physical quantity.

Unification through Generalised Proper Time: The Elementary Construction of the Theory

Unification based upon the generalisation of proper time is proposed as a comprehensive framework to account for the fundamental structure of matter, in a manner contrasting with the more familiar approach based on extra dimensions of space. The elementary properties of matter to be incorporated include the Standard Model of particle physics together with a source for the dark sector and a coherent formalism for quantum gravity. We elaborate upon the manner in which all such material phenomena and empirical properties as distributed in an extended 4-dimensional spacetime can be encompassed within, and derived from, the continuous flow of time alone via a generalised arithmetic form for infinitesimal intervals of proper time. This approach will also be compared and contrasted with the basic structure of causal set theory as a means of demonstrating how it is possible to construct a full physical theory essentially from elements of time alone, as explicitly developed from the most elementary level. The conception of time as utilised and elucidated in this theory, with emphasis upon the causal continuum properties and as the basis for unification, will be clarified.

Cosmological Perturbations via Quantum Corrections in M-Theory

In the early universe, it is important to take into account the quantum effect of gravity to explain the feature of inflation. In this paper, we consider the M-theory effective action which consists of 11-dimensional supergravity and (Weyl)4 terms. The equations of motion are solved perturbatively, and the solution describes the inflation-like expansion in 4-dimensional spacetime. Equations of motion for tensor perturbations around this background are derived perturbatively. We also check that the equations of motion are obtained from the effective action up to the second order of the perturbations. Finally, we solve the equations of motion for the tensor perturbations perturbatively and obtain analytic expressions for them.

From the BTZ black hole to JT gravity: geometrizing the island

We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view. A partial dimensional reduction of AdS3 in Poincaré coordinates leads to an extremal 2D black hole in JT gravity coupled to a ‘bath’: the holographic dual of the remainder of the 3D spacetime. Partially reducing the BTZ black hole gives us the finite temperature version. We compute the entropy of the radiation using geodesics in the three-dimensional spacetime. We then focus on the finite temperature case and describe the dynamics by introducing time-dependence into the parameter controlling the reduction. The energy of the black hole decreases linearly as we slowly move the dividing line between black hole and bath. Through a re-scaling of the BTZ parameters we map this to the more canonical picture of exponential evaporation. Finally, studying the entropy of the radiation over time leads to a geometric representation of the Page curve. The appearance of the island region is explained in a natural and intuitive fashion.

Phase transitions in the logarithmic Maxwell O(3)-sigma model

We investigate the presence of topological structures and multiple phase transitions in the O(3)-sigma model with the gauge field governed by Maxwell’s term and subject to a so-called Gausson’s self-dual potential. To carry out this study, it is numerically shown that this model supports topological solutions in 3-dimensional spacetime. In fact, to obtain the topological solutions, we assume a spherically symmetrical ansatz to find the solutions, as well as some physical behaviors of the vortex, as energy and magnetic field. It is presented a planar view of the magnetic field as an interesting configuration of a ring-like profile. To calculate the differential configurational complexity (DCC) of structures, the spatial energy density of the vortex is used. In fact, the DCC is important because it provides us with information about the possible phase transitions associated with the structures located in the Maxwell–Gausson model in 3D. Finally, we note from the DCC profile an infinite set of kink-like solutions associated with the parameter that controls the vacuum expectation value.

Exact black hole solutions with a conformally coupled scalar field and dynamic Ricci curvature in f(R) gravity theories

We report exact black hole solutions in asymptotically flat or (A)dS four-dimensional spacetime with a conformally coupled self-interacting scalar field in f(R) gravity. We first consider the asymptotically flat model $$f(R) = R -2\alpha \sqrt{R}$$ f ( R ) = R - 2 α R and derive an exact black hole solution. Then, we consider the asymptotically (A)dS model $$f(R) =R -2 \Lambda -2 \alpha \sqrt{R-4 \Lambda }$$ f ( R ) = R - 2 Λ - 2 α R - 4 Λ and derive an exact black hole solution. In both cases the modified gravity parameter $$\alpha $$ α , which has the dimension of the inverse mass, cannot be set to zero and the self-interacting potential is determined from the Klein–Gordon equation, preserving the conformal invariance. The thermodynamics of the solutions is also studied.

The Dark Sector and the Standard Model from a Local Generalisation of Extra Dimensions

Many models with structures of matter associated with a structure of extra spatial dimensions have been proposed in recent decades. On employing a further generalisation from the local 4-dimensional spacetime form to a general form for proper time, we describe how matter fields resembling the Standard Model of particle physics can be accommodated far more directly than with a higher-dimensional spacetime theory. The successful identification of key features of visible matter in this non-spatial sector of extra dimensions in turn motivates seeking a candidate for dark matter residing in the original extra spatial dimension sector, and provides a close guide for the explicit form this invisible matter might take. We describe how such Standard Model and dark matter sectors in different extra-dimensional branches of generalised proper time are gravitationally connected through their common root in the local 4-dimensional spacetime and consider further possible mutual interactions and implications in comparison with existing dark matter models. A yet further possible branch of generalised proper time can be connected with dark energy models, hence in principle accounting for all three major components of cosmological structure within this framework.

Experimental verification of the field theory of specific heat with the scaling in crystalline matter

The field (geometrical) theory of specific heat is based on the universal thermal sum, a new mathematical tool derived from the evolution equation in the Euclidean four-dimensional spacetime, with the closed time coordinate. This theory made it possible to explain the phenomena of scaling in the heat capacity of condensed matter. The scaling of specific heat of the carbon group elements with a diamond lattice is revisited. The predictions of the scaling characteristics for natural diamond and grey tin are verified with published experimental data. The fourth power in temperature in the quasi-low temperature behaviour of the specific heat of both materials is confirmed. The phenomenon of scaling in the specific heat, previously known only in glassy matter, is demonstrated for some zincblend lattice compounds and diamond lattice elements, with their characteristic temperatures. The nearly identical elastic properties of grey tin and indium antimonide is the cause for similarity of their thermal properties, which makes it possible to make conjectures about thermal properties of grey tin.

Quark-hadron duality for heavy meson mixings in the ’t Hooft model

We study local quark-hadron duality and its violation for the $$ {D}^0-{\overline{D}}^0 $$ D 0 − D ¯ 0 , $$ {B}_d^0-{\overline{B}}_d^0 $$ B d 0 − B ¯ d 0 and $$ {B}_s^0-{\overline{B}}_s^0 $$ B s 0 − B ¯ s 0 mixings in the ’t Hooft model, offering a laboratory to test QCD in two-dimensional spacetime together with the large-Nc limit. With the ’t Hooft equation being numerically solved, the width difference is calculated as an exclusive sum over two-body decays. The obtained rate is compared to inclusive one that arises from four-quark operators to check the validity of the heavy quark expansion (HQE). In view of the observation in four-dimensions that the HQE prediction for the width difference in the $$ {D}^0-{\overline{D}}^0 $$ D 0 − D ¯ 0 mixing is four orders of magnitude smaller than the experimental data, in this work we investigate duality violation in the presence of the GIM mechanism. We show that the order of magnitude of the observable in the $$ {D}^0-{\overline{D}}^0 $$ D 0 − D ¯ 0 mixing is enhanced in the exclusive analysis relative to the inclusive counterpart, when the 4D-like phase space function is used for the inclusive analysis. By contrast, it is shown that for the $$ {B}_d^0-{\overline{B}}_d^0 $$ B d 0 − B ¯ d 0 and $$ {B}_s^0-{\overline{B}}_s^0 $$ B s 0 − B ¯ s 0 mixings, small yet non-negligible corrections to the inclusive result emerge, which are still consistent with what is currently indicated in four-dimensions.