Gravity Equation Research Articles

The geometry of the Rindler black hole

Using Einstein's equations for gravity for a spherically symmetric field in a static state and the mass function method, a general form of the metric for Schwarzschild-type black holes is proposed. A qualitative analysis of Schwarzschild, Reissner–Nordström and Rindler geometries is performed. In the paper, it is found that Rindler black hole geometry is structurally inverse to Reissner–Nordström geometry, i.e. it has two T-regions and one R-region. In this regard Rindler geometry is like geometry of the Kottler black hole, which does not have flat asymptotics. Potential curves in the gravitational field of the Rindler black hole are constructed, which makes it possible to calculate the limits of finite motion for a test particle in this field. In addition, a qualitative comparison with the known Schwarzschild field metric is performed. Their similarity in behavior at small distances and absolutely different behavior at large scales are shown. Using the known accelerations of the Pioneer spacecraft, limits are numerically found for the T- and R-regions of their motion in the gravitational field of the Solar System.

The Trade Effect of Non-tariff Measures in a Comprehensive Trade Agreement

The aim of this study is to quantify the trade effects of the Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP), which is considered to be a comprehensive trade agreement. To this end, we estimate the gravity equation for worldwide trade and introduce applied tariffs into this equation to differentiate between the trade effects of tariff reduction and non-tariff measure (NTM) changes. Our gravity equation results indicate that the trade effect of NTM changes under the CPTPP is insignificant on average and negative for most products. We also estimate the gravity equation for foreign direct investment (FDI) and find some evidence that the CPTPP increased FDI by a statistically significant amount. Thus, the NTM changes in the CPTPP may increase FDI, rather than trade, among member countries.

Quantum Spacetime Geometrization: QED at High Curvature and Direct Formation of Supermassive Black Holes from the Big Bang

In this work, the author employs the quantum hydrodynamic formalism to achieve the geometrization of spacetime for describing the gravitational interaction within the framework of quantum theory. This approach allows for the development of an equation of gravity that is mathematically connected to the fermion and boson fields. This achievement is accomplished by incorporating two fundamental principles: covariance of the quantum field equations and the principle of least action. By considering these principles, a theory is established that enables the calculation of gravitational corrections to quantum electrodynamics and, potentially, to the standard model of particle physics as well. The theory also provides an explanation for two phenomena: the existence of a cosmological pressure density similar to quintessence, which is compatible with the small value of the observed cosmological constant, and the breaking of matter–antimatter symmetry at high energies, offering insights into why there is an imbalance between the two in the early universe. In the cosmological modeling of the theory, there exists a proposal to account for the formation of supermassive black holes that are accompanied by their own surrounding galaxies, without relying on the process of mass accretion. The model, in accordance with recent observations conducted by the James Webb Space Telescope, supports the notion that galactic configurations were established relatively early in the history of the universe, shortly after the occurrence of the Big Bang.

Chaplygin gas equation in curvature-matter coupling gravity

In this paper, we study the Chaplygin gas equation in curvature-matter coupling gravity to describe the observed expansion of the universe. We consider the Chaplygin gas equation of state in terms of the energy density [Formula: see text] and pressure [Formula: see text], by the relationship [Formula: see text] and the curvature-matter coupling gravity as [Formula: see text], where [Formula: see text] is a positive constant, [Formula: see text] and [Formula: see text] denote, respectively, the Ricci scalar and the trace of energy–momentum tensor. Considering the gravitational lagrangian in the form [Formula: see text], where we used two forms of [Formula: see text] and by assuming a perfect fluid as matter source, we determined through the modified Friedmann equations, the corresponding energy and pressure for each model. By using the free parameters of our models, we performed the numerical results of the energy conditions to study its viability. Furthermore, we have derived some cosmological parameters like deceleration parameter and statefinder parameters and graphically investigated the nature of these parameters in Chaplygin gas model.

Classical and quantum gravity from the axioms of relativistic quantum mechanics

It is common practice to describe elementary particles by irreducible unitary representations of the Poincaré group. In the same way, multi-particle systems can be described by irreducible unitary representations of the Poincaré group. Representations of the Poincaré group are characterised by fixed eigenvalues of two Casimir operators corresponding to a fixed mass and a fixed angular momentum. In multi-particle systems (of massive spinless particles), fixing these eigenvalues leads to correlations between the particles. In the quasi-classical approximation of large quantum numbers, these correlations take on the structure of a gravitational interaction described by the field equations of conformal gravity. A theoretical value of the corresponding gravitational constant is calculated. It agrees with the empirical value used in the field equations of general relativity.

Did Remittance Inflow in Bangladesh Follow the Gravity Path during COVID-19?

Remittances are one of the major driving forces of economic growth in Bangladesh. The paper’s main objective is to empirically investigate the effect of COVID-19 on the remittance inflow to Bangladesh using a gravity model framework. We have employed monthly data of remittance inflow to Bangladesh from January 2018 to September 2022 with its top twelve partners, namely the Kingdom of Saudi Arabia, the United Arab Emirates, Kuwait, Qatar, Oman, Bahrain, Libya, the United Kingdom, Italy, Malaysia, Singapore, and Japan. Using the gravity equation, we tapped the COVID-19 dummy as the critical variable of our interest, along with COVID transmission, mortality, and vaccination data at home and abroad. Using Poisson pseudo-maximum likelihood (PPML), fixed-effect (FE), and random-effect (RE) estimations, we find that during the COVID-19 pandemic, remittance inflow to Bangladesh increased significantly after controlling for other Gravity variables.

Risky Gravity

Abstract We consider the canonical trade model with heterogeneous firms, love for variety and trade costs, and integrate it in the consumption CAPM model. This yields a structural gravity equation that includes an additional factor related to risk premia. Empirical evidence based on firm-level data confirms the importance of cross-sectional heterogeneity in risk and time-varying risk premia to shape bilateral trade flows. The structural gravity model augmented to account for fluctuations in risk premia offers a compelling explanation for trade collapses during abrupt economic downturns.

Tariff rates in gravity

This paper considers the case where multiple tariff schemes (e.g. general and preferential schemes) are available between trading countries. We incorporate these tariffs into gravity equations and estimate them by the Pseudo-Poisson maximum likelihood technique. The results show that omitting either tariff type leads to significant estimates biases. If fixed effects to control other tariffs are not included in the model, both preferential and general tariffs are to be introduced in the gravity equation. Indeed, some estimation results for precision metals show that reducing both types of tariffs contributes to significantly increasing trade values. However, reducing general tariffs does not always have a trade-enhancing effect. In leather products, for example, its impact was insignificant. Nevertheless, the reduction of preferential tariffs was again found to increase trade values significantly.

Estimating multicountry tourism flows by transport mode

This article describes the methodology used to obtain a harmonized database of country-to-country flows of tourists and visitors built upon the UNWTO original database. Focusing on 74 countries for the period 1995–2018 and starting with data on outbound tourism, we develop a methodology using other alternative indicators from the UNWTO which fills the gaps related to two main indicators (Foreign Visitors by country of Residence and Foreign Tourists by country of Residence). Subsequently, intra-national domestic tourism and the transport mode specific flows are obtained. The paper finally contrasts the robustness of the results obtained with the gravity equation for all flows, thereby confirming the solvency of the process and the final data retrieved.

Brexit Uncertainty and Its (Dis)Service Effects

We estimate the impact of increased policy uncertainty from Brexit on UK trade in services. We apply an uncertainty-augmented gravity equation to UK services trade with the European Union at the industry level from 2016:I to 2018:IV. By exploiting the variation in the probability of Brexit from prediction markets interacted with a new trade policy risk measure across service industries, we identify a significant negative impact of the threat of Brexit on trade values and participation. The increased probability of Brexit in this period lowered services exports by at least 20 log points. (JEL F13, F14, F15)

Holographic CFTs on AdSd× Sn and conformal defects

We consider (d+n+1)-dimensional solutions of Einstein gravity with constant negative curvature. Regular solutions of this type are expected to be dual to the ground states of (d + n)-dimensional holographic CFTs on AdSd × Sn. Their only dimensionless parameter is the ratio of radii of curvatures of AdSd and Sn. The same solutions may also be dual to (d − 1)-dimensional conformal defects in holographic QFTd+n. We solve the gravity equations with an associated conifold ansatz, and we classify all solutions both singular and regular by a combination of analytical and numerical techniques. There are no solutions, regular or singular, with two boundaries along the holographic direction. Out of the infinite class of regular solutions, only one is diffeomorphic to AdSd+n+1 and another to AdSd × AdSn+1. For the regular solutions, we compute the on-shell action as a function of the relevant parameters.

International Technology Licensing, Intellectual Property Rights, and Tax Havens

Abstract This paper investigates the determinants of international technology licensing using data for 50 countries during 1996-2012. A multi-country model of innovation yields a dynamic structural gravity equation for royalty payments as a function of fundamentals, including imperfect intellectual property protection and differences in corporate taxation. The gravity equation is estimated with nonlinear methods. Model's fundamentals account for about 60% of the variation in royalty payments. A quantitative analysis sheds light on the impact of global taxation reforms on international technology licensing and innovation. The findings highlight the role of taxation in shaping cross-border technology flows and the consequences of profit-shifting.

Effect of massive graviton on dark energy star structure

The presence of massive gravitons in the field of massive gravity is considered an important factor in investigating the structure of compact objects. Hence, we are encouraged to study the dark energy star structure in the Vegh’s massive gravity. We consider that the equation of state governing the inner spacetime of the star is the extended Chaplygin gas, and then using this equation of state, we numerically solve the Tolman–Oppenheimer–Volkoff (TOV) equation in massive gravity. In the following, assuming different values of free parameters defined in massive gravity, we calculate the properties of dark energy stars such as radial pressure, transverse pressure, anisotropy parameter, and other characteristics. Then, after obtaining the maximum mass and its corresponding radius, we compute redshift and compactness. The obtained results show that for this model of dark energy star, the maximum mass and its corresponding radius depend on the massive gravity’s free parameters and anisotropy parameter. These results are consistent with the observational data and cover the lower mass gap. We also demonstrate that all energy conditions are satisfied for this model, and in the presence of anisotropy, the dark energy star is potentially unstable.

Mild Arabica coffee trade at a time of market regulation

ABSTRACT This paper explores the dynamics of mild coffee trade during the term of the International Coffee Agreement, focusing on Costa Rica as a case study. We aimed to verify the influence of the agreement on coffee exports and understand its impact on the exports of high-quality coffee. To compare the influence of the coffee agreement on the trade performance of high-quality coffee producers with that of producers specializing in coffee of similar – or lower – quality, we also included exports of Brazilian coffee (low quality) and Colombian coffee (high quality) in the sample. We focused on analysing commodity trade agreements in the second half of the twentieth century and, simultaneously, on the drivers of coffee exports based on a gravity equation consistent with international trade models. Our findings allowed us to conclude that the International Coffee Agreement gave rise to few benefits for ‘Other Milds’ countries such as Costa Rica and greater benefits for ‘Colombian Milds’ countries such as Colombia, at least in its early versions.

The Proton, Gravity, and Black Hole Equations

In these papers, I presented and explained the Potential Energy Equation "P.E.E."; this equation is about discovering how gravitation works, the cosmological facts for the Black Hole physics "B.H.", and the "B.H." primary role in the gravitational energy at both the astronomical (planets: Earth, Sun, etc.) and microscopic atomic (Protons) levels. "P.E.E." equation is uncovering a new concept for the Planck Constant and the Fine Structure, as an inhibition for the "B.H." energy and as a convertor from one type of energy to another in the "P.E.E." energies parts; this new concept is also explaining the "Attractive Mass" or "central mass" and redefining the Gravitational Potential Energy Ug ; and the Kinetic Energy as well; and it is clarifying the difference in apply between Ug and the Weak Potential Energy of mass (Attracted Mass) "Ag ". I already defined the "B.H." potential energy ( fs ) equation, the mass compressed "Np " with radius"rs " of the “B.H” equation, the mass compressing distance "rc " and the radius "rs " of the “B.H.” equation; and the gravitational and "B.H." energy equations; I have also applied these equations on astronomical and microscopic dimensions.

Italian small arms exports: between incentives and international sanctions

This paper empirically investigates the determinants of Italian Small Arms and Light Weapons (hereafter SALW) exports to 143 polities from 1990 to 2017. We focus in particular on three aspects: (1) the economic drivers of SALW exports by means of a standard gravity equation of trade; (2) the internal characteristics of the importer country, namely the degree of militarization and the attitude to violence exerted by government against citizens; (3) the impact of international constraints on SALW trade by highlighting in particular EU and UN embargoes. We estimate the empirical models for total exports but also distinguishing between the two sub-categories of military and sporting SALW. Findings highlight that (1) there is a complementarity between Italian exports and the importer’s military expenditure; (2) there is a correlation between Italian exports of SALW and both a disregard for physical integrity and a potential for military influence over the government in the importing country; (3) international embargoes reduce substantially Italian SALW exports; (4) UN and EU embargoes seem to have a different impact; (5) There is no evidence of sanctions-busting. In broader terms, this study highlights that unlike the standard patterns observed for civilian goods, political and military factors matter substantially for the international trade of SALW.

COVID‐19 and the distance effect

AbstractUsing nearly 200 countries' bilateral trade data and the gravity equation, this paper provides evidence that COVID‐19 has led countries to trade more with their closer countries. The negative distance effect is greater during the pandemic period, with a greater number of infected cases, deaths or stricter control policies. A simple model of a transportation sector that was affected by the pandemic was built to explain our empirical findings.

Empirical insights on the dynamics of SPS trade costs: The role of regulatory convergence and experience in EU dairy trade

With its influence on the world stage, the EU’s Farm to Fork initiative seeks to extend sustainable and fair food production practises globally, in part, by encouraging convergence with EU food standards (i.e., sanitary and phytosanitary measures-SPS). Harmonisation clauses have been found empirically to encourage trade, but no quantifiable estimates exist on the trade effects of SPS regulatory convergence. This paper examines this issue for the dairy industry, a highly regulated sector with significant sustainability concerns attached. Furthermore, the cost-saving effects arising from closer regulations and ‘experience’ (i.e., accumulated years of foreign trade track-record), are compared. Employing a 3-year interval panel starting in 2010, a structural gravity equation that includes domestic trade is estimated with a flexible empirical approach that evinces asymmetric trade impacts for specific bilateral trade routes. Results indicate a trade depressing effect for SPS measures, estimated as a global average 10.4% Ad-valorem Equivalent (AVE). Moreover, at the global level, converging regulatory frameworks generate larger trade gains than experience, where a 1% rise in regulatory convergence is equivalent to 5 years of positive trade and a 14% reduction of the AVE. The reduction of trade frictions prompted by harmonisation and experience does not, however, outweigh SPS trade costs. Exporters to the EU face a higher SPS AVE than that faced by the EU (10.1% vs 9.3%). On average, exporters to the EU also benefit from a 9% saving due to experience, although cost savings from regulatory convergence are only reported for larger exporters to the EU, whose consolidated position in EU markets also grants them even greater than average benefits from years of accumulated experience.

Individual preferences toward inward foreign direct investment: A survey experiment

In democratic societies, public attitudes toward foreign direct investment (FDI) can influence FDI policy as in other policy areas but have been largely ignored in FDI literature. To bridge this gap, we investigate individual preferences toward inward FDI. We employ a conjoint (vignette) survey experiment and analyze the determinants of preferences toward acquisitions by foreign firms. Conjoint survey experiments allow us to simultaneously estimate the effects of various attributes of foreign acquisitions, enabling us to analyze the complex causal relationships between various attributes of an acquisition project and people’s antipathy toward it. The results of the experiment show that the nationality of the foreign firm, reciprocity, and the economic conditions of the location of the firm being acquired are important factors. The subgroup analysis shows that older respondents and women are more negative about inward FDI. We also employ the gravity equation and confirm that our survey results are in line with the actual pattern of inward FDI stock.

The universality of black hole thermodynamics

The thermodynamic properties of black holes — temperature, entropy and radiation rates — are usually associated with the presence of a horizon. We argue that any extremely compact object (ECO) must have the same thermodynamic properties. Quantum fields just outside the surface of an ECO have a large negative Casimir energy similar to the Boulware vacuum of black holes. If the thermal radiation emanating from the ECO does not fill the near-surface region at the local Unruh temperature, then we find that no solution of gravity equations is possible. In string theory, black holes microstates are horizonless quantum objects called fuzzballs that are expected to have a surface [Formula: see text] outside [Formula: see text]; thus the information puzzle is resolved while preserving the semiclassical thermodynamics of black holes.