In the standard Einstein’s theory the exterior gravitational field of any static and axially symmetric stellar object can be described by means of a single function from which we obtain a metric into a four-dimensional space–time. In this work we present a generalization of those so called Weyl solutions to a space–time–matter metric in a five-dimensional manifold within a non-compactified Kaluza–Klein theory of gravity. The arising field equations reduce to those of vacuum Einstein’s gravity when the metric function associated to the fifth dimension is considered to be constant. The calculation of the geodesics allows to identify the existence or not of different behaviours of test particles, in orbits on a constant plane, between the two metrics. In addition, static solutions on the hypersurface orthogonal to the added dimension but with time dependence in the five-dimensional metric are also obtained. The consequences on the variation of the rest mass, if the fifth dimension is identified with it, are studied.

In this paper, we report on exact charged black hole solutions in symmergent gravity with Maxwell field. Symmergent gravity induces the gravitational constant G, quadratic curvature coefficient , and the vacuum energy from the flat spacetime matter loops. In the limit in which all fields are degenerate in mass, the vacuum energy can be expressed in terms of G and . We parametrize deviation from this limit by a parameter such that the black hole spacetime is de Sitter (dS) for and anti-de Sitter (AdS) for . In our analysis, we study horizon formation, shadow cast and gravitational lensing as functions of the black hole charge, and find that there is an upper bound on the charge. At relatively low values of charge, applicable to astronomical black holes, we determine constraints on and using the Event Horizon Telescope (EHT) data from Sgr. A* and M87*. We apply these constraints to reveal how the shadow radius behaves as the observer distance varies. It is revealed that black hole charge directly influences the shadow silhouette, but the symmergent parameters have a tenuous effect. We also explored the weak field regime by using the Gauss–Bonnet theorem to study the weak deflection angle caused by the M87* black hole. We have found that impact parameters comparable to the actual distance D = 16.8 Mpc show the potential detectability of such an angle through advanced astronomical telescopes. Overall, our results provide new insights into the behavior of charged black holes in the context of symmergent gravity and offer a new way to test these theories against observational data.

In this paper, we study rotating black holes in symmergent gravity, and use deviations from the Kerr black hole to constrain the parameters of the symmergent gravity. Symmergent gravity induces the gravitational constant G and quadratic curvature coefficient c_{textrm{O}} from the flat spacetime matter loops. In the limit in which all fields are degenerate in mass, the vacuum energy V_{textrm{O}} can be wholly expressed in terms of G and c_{textrm{O}}. We parametrize deviation from this degenerate limit by a parameter {hat{alpha }} such that the black hole spacetime is dS for {hat{alpha }} < 1 and AdS for {hat{alpha }} > 1. In constraining the symmergent parameters c_{textrm{O}} and {hat{alpha }}, we utilize the EHT observations on the M87* and Sgr. A* black holes. We investigate first the modifications in the photon sphere and shadow size, and find significant deviations in the photonsphere radius and the shadow radius with respect to the Kerr solution. We also find that the geodesics of time-like particles are more sensitive to symmergent gravity effects than the null geodesics. Finally, we analyze the weak field limit of the deflection angle, where we use the Gauss-Bonnet theorem for taking into account the finite distance of the source and the receiver to the lensing object. Remarkably, the distance of the receiver (or source) from the lensing object greatly influences the deflection angle. Moreover, c_{textrm{O}} needs be negative for a consistent solution. In our analysis, the rotating black hole acts as a particle accelerator and possesses the sensitivity to probe the symmergent gravity.

The Karolyhazy uncertainty relation states that if a device is used to measure a length l, there will be a minimum uncertainty \(\delta l\) in the measurement, given by \((\delta l)^3 \sim L_{\mathrm {P}}^2 l\). This is a consequence of combining the principles of quantum mechanics and general relativity. In this letter we show how this relation arises in our approach to quantum gravity, in a bottom-up fashion, from the matrix dynamics of atoms of space–time–matter. We use this relation to define a space–time–matter (STM) foam at the Planck scale, and to argue that our theory is holographic. By coarse graining over time-scales larger than Planck time, one obtains the laws of quantum gravity. Quantum gravity is not a Planck scale phenomenon; rather it comes into play whenever classical space–time background is not available to describe a quantum system. Space–time and classical general relativity arise from spontaneous localisation in a highly entangled quantum gravitational system. The Karolyhazy relation continues to hold in the emergent theory. An experimental confirmation of this relation will constitute a definitive test of the quantum nature of gravity.

The geometrization of quantum mechanics, the nonlinear Klein–Gordon equation, Finsler gravity and phase spaces

The world has been taking a new turn. Humanity has been crossing the threshold to emerge as Homo spiritualis! Spiritual quest of a large number of scientists has been taking the science beyond materialism; science with space time matter and visible energy. Galileo Commission of Scientific and Medical Network, UK has been working hard to extend the scope of science by extending its horizon, by pushing the envelope.

Dark matter = modified gravity? Scrutinising the spacetime–matter distinction through the modified gravity/ dark matter lens

Cartography of the space of theories: An interpretational chart for fields that are both (dark) matter and spacetime

Abstract Drawing on posthumanist and new materialism theorising, we take the concept of resonance for an a/r/tographic ‘walk’ to know, be and do differently, to challenge human-centric separatist ways that have resulted in our current socioecological crises. Beginning with Ingold’s knotty thinking, we identify the notion of resonance as a node for exploring and thinking about interactions in the world. Guided by Barad’s proposition of entangling ethico-onto-epistemic ways, our a/r/tographic thought experiments find resonances that echo through bodies, through connections as nature, through deep-time and modern spaces to notice and attend to intraactions within the ecological collective. Through art-full, thought-full scholartistic enquiry, we explore diffractive encounters to consider resonance as a conceptual tool for tuning into and harmonising with the entanglements of body–mind–space–time–matter. We pose this exploration of resonance as the start of a knotty theory conversation for shifting into a new ‘common world’ knowing, being and doing.

In our recently proposed quantum theory of gravity, the universe is made of ‘atoms‘” of space-time-matter (STM). Planck scale foam is composed of STM atoms with Planck length as their associated Compton wave-length. The quantum dispersion and accompanying spontaneous localization of these STM atoms amounts to a cancellation of the enormous curvature on the Planck length scale. However, an effective dark energy term arises in Einstein equations, of the order required by current observations on cosmological scales. This happens if we propose an extremely light particle having a mass of about [Formula: see text], forty-two orders of magnitude lighter than the proton. The holographic principle suggests there are about [Formula: see text] such particles in the observed universe. Their net effect on space-time geometry is equivalent to dark energy, this being a low energy quantum gravitational phenomenon. In this sense, the observed dark energy constitutes evidence for quantum gravity. We then invoke Dirac’s large number hypothesis to also propose a dark matter candidate having a mass halfway (on the logarithmic scale) between the proton and the dark energy particle, i.e. about [Formula: see text].

In this paper, I explain how I engaged with walking as a sensory and relational inquiry that provoked thinking differently and intra-actively of research, and the entanglement (Barad, 2007) of our bodies with the space and matter. As I walked the city of Memphis, assemblages of my emplaced body movement, subjectivities, senses, feelings, and interactions with the materiality of the space deconstructed and interrogated the neoliberal normalized narratives of othering and belonging. Situating the walks within transcorporeality (Alaimo, 2012), transmateriality (Springgay &amp; Truman, 2017a), and the spactimematter entanglement (Haraway, 2015), I share how these walks generated three lines of flight (Deleuze &amp; Guattari,1987) that transformed my thinking of research methods and opened up spaces for new ways of knowing beyond the linear and the prescribed. The three lines of flight, I discuss in this paper, informed and shaped my thinking of: my research methods with respect to interviewing Muslim American youth, the embodied experience of walking within the entanglement of space time matter in a more-than-human world, and the concept of (dis)placed bodies within the postcolonial thought.

Background. I.Stravinsky’s orchestration is quite an original phenomenon; its essential characteristics are influenced not only by objective intra-musical factors (reconfiguration of musical language on the verge of XIX–XX centuries) or by subjective individual and stylistic determinants, but also by the changes, which occurred in the cultural context of the first half of XX century under influence of scientific and technical progress (Arkadev, 1992; Gerasimova-Persidskaya, 2012). The first two decades of XX century became the time, when the new generation of composers emerged, who reflected complexity of the world and different understanding of temporal and spatial relations in sound matter of their works. First, we mean C. Debussy, I. Stravinsky, the composers of the Second Viennese School and B. Bart&amp;#243;k. Objectivation of the worldview largely influenced the orchestration as it is one of the means to organise musical matter in space-time. Literature review. Orchestration by I. Stravinsky is the object of research in the articles of V. Gurkov (1987) and A. Schnittke (1967; 1973). Valuable observation and commentary on composer’s orchestration are found in several monographs (Asafev, 1977; Baeva, 2009; Druskin, 2009; Savenko, 2001; Yarustovskiy, 1982). In the available works, orchestral writing by I. Stravinsky has not been examined, especially in the aspect of its constant principles. Results. Concept of “orchestral writing” needs to be clarified; it is widely used, although scarcely developed. We suggest our own definition of this concept. Orchestral writing is an individual system of technological devices and principles, determined by composer’s musical language and common, basic rules of orchestration, aimed at realisation of timbre and textural aspects of the work, conditioned by style, genre and artistic idea and incarnated in functional interaction of orchestral parts in horizontal and vertical axes. General principles of I. Stravinsky’s orchestral writing became discernible in his early works; we define them as multi-figure composition, combinatorics and plastique. Combinatorics can be understood as universal principle of I. Stravinsky’s compositional method and orchestral writing, which affects all the levels of compositional whole, the work itself. Combinatorics is widely used in visual arts, where it is interpreted as a method to find various combinations through rearrangements, moving, different configurations of given elements, their juxtaposition in a certain order. Used as a term to define orchestral writing, combinatorics supposes manipulation with small timbre and textural elements and structures; this is conditioned by type of the themes, used by the composer as well as by variability of intervals and motives. Frequent succession of thematic structures causes rushed tempo of changes of timbre and textural structures, which, in its turn, causes musical time to be densely filled with informational events, and musical space became heterogeneous, contrasting, motley. Combinatorics is embodied in such tools as timbre transmissions and switching, when thematic structures distributed between several timbre groups by the means of split, handoff or juxtaposition, combination of orchestral groups, while remaining in the same structural and compositional section; as a rule, this does not result in a change of orchestral texture. This engenders mosaic-like orchestration, intense contrasts of timbre. Combinatorics in I. Stravinsky’s scores is skillfully realized through increase and decrease in quantity of voices (timbres) in horizontal and vertical axes. In vertical axis it is achieved by usage of incomplete and inexact (fragmentary, variable) doubles, having role of timbre “highlighting”, creating timbre variants of the main line, filling orchestral texture with unremitting timbre move and spatiality. As fragmentary and variable doubles are used, density of the texture is regulated through pauses in doubling lines; thus, the composer avoids risk of overloading the texture. In horizontal axis combinatorics causes alternation of timbres and timbre mixtures within rather shorts periods of musical time with the same orchestral texture, which causes constant timbre development and indicates wise usage of orchestral resources. In the light of combinatorics it is possible to examine and a type of orchestral tutti, raising on the basis of multi-layered orchestral texture, composed from several timbre and textural strata. Conclusions. Continuous usage of combinatorics allows to interpret it not only as constant principle of I. Stravinsky’s orchestral writing, but also as “universal” (according to definition of S. Savenko, 2001) in composer’s orchestral thinking. The same can be applied to such principles as multi-figure and plastique. Their interaction spawns diverse combinations in the Stravinsky’s compositions of the “Russian”, “Neo-Classical” and late stages of his creativity, their influence might be either conspicuous or hidden. Abovementioned principles are used to different extent in each case, depending on the type of space-time that I. Stravinsky employs in the works of different periods: time filled with events and motley, heterogeneous space in the works of the “Russian” period; relatively continuous time, rich with information and events, and more homogenous space in the works of the “Neo-Classical” period; Eternity and simultaneous usage of different time models and strictly geometrical (pure in its abstractness) Space in the works of the late period.

Wormholes (WHs) are considered as hypothetical shortcuts or tunnels in spacetime. In general relativity (GR), the fundamental ingredient of WH geometry is the presence of exotic matter at the throat, which is responsible for the violation of null energy condition (NEC). However, the modified gravity theories have shown to be able to provide WH solutions satisfying energy conditions (ECs). In this paper, we study the static spherically symmetric WH solutions in modified [Formula: see text] gravity for a phantom fluid case. The exact solutions of this model are obtained through the equation of state (EoS), [Formula: see text], associated with phantom dark energy (DE) [Formula: see text]. We find the existence of spherically symmetric WH solution supported by phantom energy distribution. The shape function of the WH obtained in this model obeys all the WH metric conditions. In modified gravity scenario, the phantom fluid WH violates the NEC in radial case, unlike in the tangential case. Furthermore, using the “volume integral quantifier” (VIQ) method, the total amount of EC violating matter in spacetime is discussed briefly.

Starting with a brief description of Born’s reciprocal relativity theory (BRRT), based on a maximal proper force, maximal speed of light, and inertial and non-inertial observers, we derive the exact thermal relativistic corrections to the Schwarzschild, Reissner–Nordstrom, and Kerr–Newman black hole entropies and provide a detailed analysis of the many novel applications and consequences to the physics of black holes, quantum gravity, minimal area, minimal mass, Yang–Mills mass gap, information paradox, arrow of time, dark matter, and dark energy. We finish by outlining our proposal towards a space–time–matter unification program where matter can be converted into spacetime quanta and vice versa.

Abstract We present a new, falsifiable quantum theory of gravity, which we name non-commutative matter-gravity. The commutative limit of the theory is classical general relativity. In the first two papers of this series, we have introduced the concept of an atom of space-time-matter (STM), which is described by the spectral action in non-commutative geometry, corresponding to a classical theory of gravity. We used the Connes time parameter, along with the spectral action, to incorporate gravity into trace dynamics. We then derived the spectral equation of motion for the gravity part of the STM atom, which turns out to be the Dirac equation on a non-commutative space. In the present work, we propose how to include the matter (fermionic) part and give a simple action principle for the STM atom. This leads to the equations for a quantum theory of gravity, and also to an explanation for the origin of spontaneous localisation from quantum gravity. We use spontaneous localisation to arrive at the action for classical general relativity (including matter source) from the action for STM atoms.

There ought to exist a reformulation of quantum theory which does not depend on classical time. To achieve such a reformulation, we introduce the concept of an atom of space-time-matter (STM). An STM atom is a classical noncommutative geometry (NCG), based on an asymmetric metric, and sourced by a closed string. Different such atoms interact via entanglement. The statistical thermodynamics of a large number of such atoms gives rise, at equilibrium, to a theory of quantum gravity. Far from equilibrium, where statistical fluctuations are large, the emergent theory reduces to classical general relativity. In this theory, classical black holes are far from equilibrium low entropy states, and their Hawking evaporation represents an attempt to return to the [maximum entropy] equilibrium quantum gravitational state.

Abstract In the first article of this series, we have introduced the concept of an atom of space-time-matter (STM), which is described by the spectral action of noncommutative geometry, corresponding to a classical theory of gravity. In the present work, we use the Connes time parameter, along with the spectral action, to incorporate gravity into trace dynamics. We then derive the spectral equation of motion for the STM atom, which turns out to be the Dirac equation on a noncommutative space.

Abstract We recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu–Goto + Kalb–Ramond string [R. T. Hammond, Rep. Prog. Phys. 65, 599 (2002)]. We explain why this is a significant gravitational theory and in what sense classical general relativity is an approximation to it. We propose that a noncommutative generalisation of this theory (in the sense of Connes’ noncommutative geometry and Adler’s trace dynamics) is a “quantum theory of gravity.” The theory is in fact a classical matrix dynamics with only two fundamental constants – the square of the Planck length and the speed of light, along with the two string tensions as parameters. The guiding symmetry principle is that the theory should be covariant under general coordinate transformations of noncommuting coordinates. The action for this noncommutative torsion gravity can be elegantly expressed as an invariant area integral and represents an atom of space–time–matter. The statistical thermodynamics of a large number of such atoms yields the laws of quantum gravity and quantum field theory, at thermodynamic equilibrium. Spontaneous localisation caused by large fluctuations away from equilibrium is responsible for the emergence of classical space–time and the field equations of classical general relativity. The resolution of the quantum measurement problem by spontaneous collapse is an inevitable consequence of this process. Quantum theory and general relativity are both seen as emergent phenomena, resulting from coarse graining of the underlying noncommutative geometry. We explain the profound role played by entanglement in this theory: entanglement describes interaction between the atoms of space–time–matter, and indeed entanglement appears to be more fundamental than quantum theory or space–time. We also comment on possible implications for black hole entropy and evaporation and for cosmology. We list the intermediate mathematical analysis that remains to be done to complete this programme.

Measuring the decay constant of 87Rb: Is the decay in radioisotopes linear? Manifestation and disintegration of the matter in space-time, and age of the Universe

Starting with the study of the geometry on the cotangent bundle (phase space), it is shown that the maximal proper force condition, in the case of a uniformly accelerated observer of mass [Formula: see text] along the [Formula: see text] axis, leads to a minimum value of [Formula: see text] lying [Formula: see text] the Rindler wedge and given by the black hole horizon radius [Formula: see text]. Whereas in the uniform circular motion case, we find that the maximal proper force condition implies that the radius of the circle cannot exceed the value of the horizon radius [Formula: see text]. A correspondence is found between the black hole horizon radius and a singularity in the curvature of momentum space. The fact that the geometry (metric) in phase spaces is observer-dependent (on the momentum of the massive particle/observer) indicates further that the matter stress energy tensor and vacuum energy in the underlying space-time may admit an interpretation in terms of the curvature in momentum spaces. Some final comments are made pertaining to the Asymptotic Safety program in gravity and why phase space geometry seems to be a proper arena for a space–time–matter unification.