An auxiliary metric (reference metric) is inevitable in massive gravity theory. In the scenario of gauge/gravity duality, with a singular reference used to study momentum dissipation, which describes electric and heat conductivity for normal conductors. We demonstrate detail that de Rham-Gabadadze-Tolley (dRGT) ghost free.

We obtain the Misner-Sharp mass in massive gravity for a four-dimensional spacetime with two-dimensional maximally symmetric subspace via inverse unified first law method. Significantly, stress energy is conserved this case general reference metric. Based on property, we confirm derived by charge find that existence of does not lead to extra constraint gravity, which notable modified gravities. In addition, as special case, also investigate static spacetime. make concise discussion stability...

We study the Misner-Sharp mass for $f(R)$ gravity in an $n$-dimensional (n$\geq$3) spacetime which permits three-type $(n-2)$-dimensional maximally symmetric subspace. obtain via two approaches. One is inverse unified first law method, and other conserved charge method by using a generalized Kodama vector. In approach, we assume still holds gravity, requires quasi-local form (We define it as mass). second corresponding to local vector mass. The approaches are equivalent, bridged constraint....

Abstract We define thermodynamic pressure P by work density W as the conjugate quantity of volume V from field equation. derive equations state = ( , T ) for Friedmann–Robertson–Walker (FRW) universe in Einstein gravity and a modified respectively. find that equation shows no - phase transition, while does, where critical exponents are same those mean theory.

Dynamical solutions are always of interest to people in gravity theories. We derive a series generalized Vaidya the $n$-dimensional de Rham-Gabadadze-Tolley massive with singular reference metric. Similar case Einstein gravity, solution can describe shining/absorbing stars. Moreover, we also find more general Vaidya-like by introducing generic matter field than pure radiation original spacetime. As result, above is naturally included this as special case. investigate thermodynamics for...

We obtain the Schwarzschild solution from thermodynamic considerations using assumptions of a quasilocal mass form (the Misner-Sharp mass) and geometric surface gravity in spherically symmetric space-time. The deduction is extended to other cases such as de Sitter, anti--de Reissner-Nordstr\"om, higher-dimensional space-times. This paper demonstrates simple hypotheses these known solutions via thermodynamics, where essentially for an adiabatic system.

The perihelion precession and deflection of light have been investigated in the 4-dimensional general spherically symmetric spacetime, master equation is obtained. As application this equation, Reissner-Nordstorm-AdS solution Clifton-Barrow in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>gravity taken as examples. We find that both electric charge...

Investigation of quasibound states black holes is significant for expected ultralight particles, as well through gravitational waves. We first investigate a massive scalar field dilatonic charged via numerical analysis. study the complex eigenfrequencies in wide range fine structure constant $\ensuremath{\mu}M$ detail, and show effects charge. Further, we an analytical approach by matching near horizon solution far solution, find its spectra excited iteration method. demonstrate that...

In a recent work, we present new point of view to the relation gravity and thermodynamics, in which derive \sch~solution through thermodynamic laws by aid Misner-Sharp mass an adiabatic system. this paper continue investigate between thermodynamics for obtaining solutions via thermodynamics. We generalize our studies on gravi-thermodynamics Einstein modified theories. By using first law with assumption that is system, reproduce Boulware-Deser-Cai solution Guass-Bonnet gravity. Using thought,...

The thin dielectric sheet-based surface integral equation (SIE) method is introduced to the accurate simulation of fracture scattering, which an important and challenging topic in hydrocarbon exploration. In proposed method, equivalent volume current decomposed into constant normal current. With this decomposition, D-field degenerates SIE, makes our stable, accurate, efficient at low frequency. Numerical results have demonstrated its excellent performance.

In the three-dimensional pure Einstein gravity, geometries of vacuum space-times are always trivial, and gravitational waves (gravitons) strictly forbidden. For first time, we find a circularly symmetric black hole with nontrivial in $f(R)$ gravity theory, which true singularity appears. this frame geometry, perturbative wave does exist. Beyond level, make constructive proof existence where Birkhoff-like theorem becomes invalid. We two classes exact solutions radiation absorption.

A bstract We make a first principle study of gravitational pressure in cosmic thermo- dynamics. The is directly derived from the unified law, fact Einstein field equation spherically symmetric spacetime. By using this pressure, we obtain thermodynamics for FRW universe, especially presenting state spacetime itself, i.e. P = ( R , T ) time. Furthermore, Joule-Thomson expansion as an application thermodynamic to find cooling-heating property universe. demonstrate that there inversion...

In this work, we report the replication and characterization of compound eye a fruit fly for imaging purpose. replication, soft lithography method was employed to replicate into UV-curable polymer. The demonstrated be effective is replicated polymer (NOA78) where each ommatidium has diameter about 30 μm sag height 7 μm. To characterize its optical property, point spread function tested NA 0.386 been obtained polymeric ommatidium. Comparing with real which measured 0.212, much larger due...

Gravitational lensing is one of the most impressive celestial phenomena, which has interesting behaviors in its strong field limit. Near such limit, Bozza finds that deflection angle light well-approximated by a logarithmic term and constant term. In this way he explicitly derived analytic expressions angles for few types black holes. paper, we study explicit calculation to two new metrics limit: (i) Schwarzschild metric extended with an additional $r^{-n}(n\geq 3)$ function; (ii)...

Wave propagations in the presence of black holes is a significant problem both theoretical and observational aspects, especially after discovery gravitational wave confirmation holes. We study scattering massless scalar field by charged dilatonic hole frame full theory. apply partial method to obtain cross sections field, investigate how charge affects sections. Furthermore, we Regge pole approach section hole. find that order results at same precision, need more poles as increases. compare...

We propose a Cosmological Model Independent Time Delay (CMITD) method where the Lorentz invariance violation (LIV) variable K(z) is constructed by observational data instead of cosmological model. The simulated time delay show CMITD could present validity LIV test. And, errors in propagating process critical for existence and magnitude LIV.

A new brane world in the sourced-Taub background is proposed. The gravity field equations internal source region and external vacuum are investigated, respectively. We find that equation of state for effective dark energy a dust can cross phantom divide w=−1. Furthermore, there drop on H(z) diagram, which presents possible mechanism recent direct data H(z).

The conformal gravity remarkably boosts our prehension of theories. We find a series dynamical solutions in the $W^2$-conformal gravity, including generalized Schwarzschild-Friedmann-Robertson-Walker (GSFRW), charged (CGSFRW), especially rotating Friedmann-Robertson-Walker (RFRW), (CRFRW), and cylindrically symmetric solutions. RFRW, CRFRW are never found Einstein modified gravities. GSFRW CGSFRW take different forms from corresponding gravity.

Separately, neither electromagnetic (EM) observations nor gravitational wave (GW) can distinguish between the $f(T)$ model and $\Lambda$CDM effectively. To break this degeneration, we simulate GW measurement based on coming observation facilities, explicitly Einstein Telescope. We make cross-validations simulated data factual EM data, including Pantheon, H(z), BAO CMBR results show that they are consistent with each other. Anyway, itself have $H_0$ tension problem which plays critical role...

Liquid composite moulding (LCM) has been successfully used to manufacture natural fiber reinforced composites. Effects of liquid absorption and swelling on the permeability fabrics in LCM were investigated. It shows that saturated measured corn syrup is 23.1%–69.5% smaller than motor oil because reduced porosity flow paths caused by swelling. Based traditional models considering effects jute fibers, a mathematic model was developed predict variable during mold filling. Experimental results...